This thesis investigates various rigidity and flexibility phenomena of convex projective structures on hyperbolic manifolds, particularly in dimension 3. Let M[superscipt n] be a finite volume hyperbolic n-manifold where [mathematical equation] and [mathematical symbol] be its fundamental group. Mostow rigidity tells us that there is a unique conjugacy class of discrete faithful representation of [mathematical symbol] into PSO(subscript n, 1). In light of this fact we examine when this representations can be non-trivially deformed into the larger Lie group of PGL[subscript n+1](R) as well as the relationship between these deformations and convex projective structures on M. Specifically, we show that various two-bridge knots do not admit such deformations into PGL[subscript 4](R) satisfying certain boundary conditions. We subsequently use this result to show that certain orbifold surgeries on amphicheiral knot complements do admit deformations. / text

Made available in DSpace on 2014-06-11T19:26:09Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-06-02Bitstream added on 2014-06-13T20:54:11Z : No. of bitstreams: 1 zanni_wa_me_jabo.pdf: 593705 bytes, checksum: 4c80e95813b3daf2b898776e4f2a056a (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Este trabalho teve o objetivo de avaliar a estabilidade e a adaptabilidade de 50 genótipos de soja [Glycine max (L.) Merrill], sendo 46 linhagens precoces, pertencente ao programa de melhoramento de soja da UNESP/FCAV- Jaboticabal, SP em parceria com a APTA (Agência Paulista de Tecnologia dos Agronegócios) e cinco cultivares comercialmente utilizadas, em dez ambientes no Estado de São Paulo. Os experimentos foram conduzidos nas safras agrícolas 2006/2007, 2007/2008, 2008/2009 e 2009/2010. O delineamento experimental foi o de blocos ao acaso, com três repetições. Foram realizadas análises individuais e conjunta, considerando o número de dias para a maturidade (NDM), altura da planta na maturidade (APM), acamamento (Ac), valor agronômico (VA) e produtividade de grãos (PG) nos diferentes locais. A estabilidade e a adaptabilidade dos genótipos foram avaliadas pelos métodos de Wricke (1965), Eberhart e Russel (1966), Lin e Binns (1988) e Annicchiarico (1992). As linhagens avaliadas apresentou-se com bom desempenho e aptidão para cultivo em áreas de reformas com cana-de-açúcar, destacando-se os genótipos 12 (JAB.00-03), 29 (JAB.00-06), 30 (JAB.00-06), 31 (JAB.00-02), 32 (JAB.00-02), 44 (JAB.00-02) e 45 (JAB.00-02) e as cultivares 48 (COODETEC 205) e 50 (IAC-FOSCARIN 31) os quais apresentaram boa estabilidade fenotípica e em média, elevada produtividade de grãos. As metodologias de estabilidade e adaptabilidade fenotípica utilizadas foram eficientes quanto à discriminação dos melhores genótipos precoces de soja / This work aimed to evaluate the stability and adaptability of 50 soybean genotypes [Glycine max (L.) Merr.], being 46 strains belonging to the breeding program for soybean UNESP/FCAV- Jaboticabal, SP in partnership with APTA (Agency Paulista Agribusiness Technology) and five cultivars used commercially in ten environments in the State of São Paulo. The experiments were conducted in the growing seasons 2006/2007, 2007/2008, 2008/2009 and 2009/2010. The experimental design was randomized blocks with three replications. Analysis were performed individual and joint, considering the number of days to maturity (NDM), plant height at maturity (APM), lodging (Ac), agronomic value (AV) and seed yield (PG) in different locations. The stability and adaptability of genotypes were evaluated by methods Wricke (1965), Eberhart and Russell (1966), Lin and Binns (1988) and Annicchiarico (1992). The strains evaluated presented with good performance and suitability for cultivation in areas of reforms with cane sugar, highlighting the genotypes 12 (JAB.00-03), 29 (JAB.00-06), 30 (JAB .00-06), 31 (JAB.00-02), 32 (JAB.00-02), 44 (JAB.00-02) and 45 (JAB.00-02) and 48 cultivars (COODETEC 205) and 50 (Foscarini IAC-31) which showed good stability phenotypic , high grain yield. The methodologies used phenotypic stability and adaptability were efficient as the best discrimination of soybean genotypes

Orientador: Rinaldo Cesar de Paula / Resumo: RESUMO – O eucalipto é a cultura de maior destaque para o setor florestal brasileiro. No entanto, a expansão do setor para áreas com condições climáticas limitantes ao desenvolvimento da cultura e a instabilidade climática atual, são alguns dos fatores que têm comprometido o desenvolvimento desta cultura no país nos últimos anos. Assim, é importante a busca contínua por ferramentas que possibilitem a prognose de crescimento, a seleção de indivíduos e famílias e a análise do comportamento de genótipos de eucalipto frente às variações ambientais de forma cada vez mais acurada. Desta forma, o objetivo geral deste trabalho foi testar o desempenho das Redes Neurais Artificiais (RNA) na modelagem de crescimento de clones de eucalipto, na predição de valores genéticos de indivíduos e famílias, e na seleção quanto à produtividade, estabilidade e adaptabilidade de progênies de Eucalyptus sp. Para a prognose de crescimento foram utilizados dados de 18 clones comerciais de Eucalyptus em diferentes estados do Brasil, e para a estimação de valor genético e análise de produtividade, estabilidade e adaptabilidade foram utilizados dados de testes de progênies de Eucalyptus grandis. Neste trabalho foram testadas diferentes arquiteturas de RNA do tipo múltiplas camadas com o algoritmo de aprendizado de retropropagação do erro e função de ativação do tipo tangente hiperbólica. O modelo desenvolvido para prognose do diâmetro à altura do peito (DAP) de árvores individuais em um local foi capaz de... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: ABSTRACT – Eucalyptus is the most important crop of the most important for the Brazilian forest sector. However, the expansion of the sector to areas with climatic conditions limiting the development of the crop and current climate instability are some of the factors that have compromised the development of this culture in the country in recent years. Thus, it is important to continuously search for tools that allow the prognosis of growth, the selection of individuals and families and the analysis of the behavior of eucalyptus genotypes in the face of environmental changes in an increasingly accurate way. Thus, the general objective of this work was to test the performance of artificial neural networks (ANN) in the modeling of growth of eucalyptus clones, prediction of genetic values of individuals and families, and selection of productivity, stability and adaptability of progenies of Eucalyptus sp. For the prognosis of growth, data from 18 commercial Eucalyptus clones were used in different states of Brazil, and for genetic value estimation and productivity, stability and adaptability analysis data from Eucalyptus grandis progenies were used. In this work, different ANN architectures of the multilayer type were tested with the backpropagation error algorithm and hyperbolic tangent activation function. The model developed for prognosis of the diameter at breast height (DBH) individual trees in one place was able to maintain good accuracy when applied at other sites. The thre... (Complete abstract click electronic access below) / Doutor

Flax is often considered a total utilization crop because of the potential to extract value from two distinct products - seeds and stem fibres. However, very little genetic information is available on flax fibre genetics in comparison to oil improvement studies. In order to gain a detailed understanding of genetic control of the fibre concentration and search for the possibilities of developing dual purpose flax lines using both seed oil and stem fibre, the following studies were initiated: The first study evaluated the fibre and oil-related traits in a recombinant inbred population derived from a cross between a fibre flax variety Viking and an oilseed flax genotype E1747 over multiple locations under western Canadian field conditions. The study confirmed the presence of a significant genotype by environment interaction (p < 0.01) for fibre concentration indicating selection for this trait will be challenging. However, a lack of significant correlation between fibre and oilseed characteristics in field trials was encouraging and strengthened the hypothesis that breeding dual purpose flax types for western Canada is possible. The study also identified potential recombinant inbred lines (RILs) with enhanced fibre concentration as well as oil characteristics for use in future breeding endeavors. The second study established an anatomical basis for further research into flax fibre improvement by studying differences between the stem anatomy of 14 diverse flax genotypes in the field and under controlled environments such as a growth chamber. The results from the study supported the use of controlled environments for the purpose of quick screening of high fibre containing genotypes, especially at the green capsule stage of plant growth. The results also indicated that it was possible to select high fibre oilseed flax lines based on anatomical markers such as average area of single fibre cells, total fibre area and fibre to stem area ratio. In the third study, 17 simple sequence repeat (SSR) and 2 cleaved amplified polymorphic sequences (CAPS) molecular markers were used to assess the extent of genetic variability in the Viking × E1747 RIL population. CAPS markers LuFAD3A and LuFAD3B had the highest marker trait association (p < 0.0001) with linoleic and linolenic acid concentration. SSR markers such as CV8824, 5B6 and LU32 were found to be associated with plant height, oil concentration and protein concentration respectively using single marker analysis and step wise regression analysis. The molecular study confirmed the importance of Viking × E1747 mapping population in identifying genes/ markers related to both fibre and oilseed related traits in flax. In the fourth study, global transcript profiling using cDNA - based microarrays was performed to identify differentially expressed fibre related transcripts between Viking and E1747. The largest group of transcripts (7 %) found more abundant in Viking relative to E1747 fell under the functional group of cell wall development using gene ontology (GO) analysis. Transcripts such as callose synthases, expansins, cytochrome P450, fasciclin-like arabino galactan proteins and β-galactosidases were highly abundant in Viking relative to E1747. The transcripts more abundant in E1747 relative to Viking were UDP – glucose glucosyltransferase, auxin repressed protein, ubiquitin conjugating enzyme, peroxidases and lipid transfer proteins. Quantitative real time PCR results confirmed the suitability of the microarray platform to accurately discriminate transcript profiles between the two diverse flax types. In conclusion, this research has provided a number of new insights into flax fibre genetics. This information lays the foundation for further genetic studies on flax bast fibres and will complement research on developing dual purpose flax varieties.

Resumo: Este trabalho teve o objetivo de avaliar a estabilidade e a adaptabilidade de 50 genótipos de soja [Glycine max (L.) Merrill], sendo 46 linhagens precoces, pertencente ao programa de melhoramento de soja da UNESP/FCAV- Jaboticabal, SP em parceria com a APTA (Agência Paulista de Tecnologia dos Agronegócios) e cinco cultivares comercialmente utilizadas, em dez ambientes no Estado de São Paulo. Os experimentos foram conduzidos nas safras agrícolas 2006/2007, 2007/2008, 2008/2009 e 2009/2010. O delineamento experimental foi o de blocos ao acaso, com três repetições. Foram realizadas análises individuais e conjunta, considerando o número de dias para a maturidade (NDM), altura da planta na maturidade (APM), acamamento (Ac), valor agronômico (VA) e produtividade de grãos (PG) nos diferentes locais. A estabilidade e a adaptabilidade dos genótipos foram avaliadas pelos métodos de Wricke (1965), Eberhart e Russel (1966), Lin e Binns (1988) e Annicchiarico (1992). As linhagens avaliadas apresentou-se com bom desempenho e aptidão para cultivo em áreas de reformas com cana-de-açúcar, destacando-se os genótipos 12 (JAB.00-03), 29 (JAB.00-06), 30 (JAB.00-06), 31 (JAB.00-02), 32 (JAB.00-02), 44 (JAB.00-02) e 45 (JAB.00-02) e as cultivares 48 (COODETEC 205) e 50 (IAC-FOSCARIN 31) os quais apresentaram boa estabilidade fenotípica e em média, elevada produtividade de grãos. As metodologias de estabilidade e adaptabilidade fenotípica utilizadas foram eficientes quanto à discriminação dos melhores genótipos precoces de soja / Abstract: This work aimed to evaluate the stability and adaptability of 50 soybean genotypes [Glycine max (L.) Merr.], being 46 strains belonging to the breeding program for soybean UNESP/FCAV- Jaboticabal, SP in partnership with APTA (Agency Paulista Agribusiness Technology) and five cultivars used commercially in ten environments in the State of São Paulo. The experiments were conducted in the growing seasons 2006/2007, 2007/2008, 2008/2009 and 2009/2010. The experimental design was randomized blocks with three replications. Analysis were performed individual and joint, considering the number of days to maturity (NDM), plant height at maturity (APM), lodging (Ac), agronomic value (AV) and seed yield (PG) in different locations. The stability and adaptability of genotypes were evaluated by methods Wricke (1965), Eberhart and Russell (1966), Lin and Binns (1988) and Annicchiarico (1992). The strains evaluated presented with good performance and suitability for cultivation in areas of reforms with cane sugar, highlighting the genotypes 12 (JAB.00-03), 29 (JAB.00-06), 30 (JAB .00-06), 31 (JAB.00-02), 32 (JAB.00-02), 44 (JAB.00-02) and 45 (JAB.00-02) and 48 cultivars (COODETEC 205) and 50 (Foscarini IAC-31) which showed good stability phenotypic , high grain yield. The methodologies used phenotypic stability and adaptability were efficient as the best discrimination of soybean genotypes / Orientador: Sandra Helena Unêda-Treviso / Coorientador: Antonio Orlando Di Mauro / Banca: Rinaldo Cesar de Paula / Banca: José Baldin Pinheiro / Mestre

Submitted by Marco Antônio de Ramos Chagas (mchagas@ufv.br) on 2018-06-14T18:06:34Z No. of bitstreams: 1 texto completo.pdf: 459927 bytes, checksum: 499f8409fc0463528b7d65b6f83d2535 (MD5) / Made available in DSpace on 2018-06-14T18:06:34Z (GMT). No. of bitstreams: 1 texto completo.pdf: 459927 bytes, checksum: 499f8409fc0463528b7d65b6f83d2535 (MD5) Previous issue date: 2018-02-23 / Conselho Nacional de Desenvolvimento Científico e Tecnológico / O sorgo granífero é considerado o quinto cereal mais cultivado no mundo, sendo uma importante fonte calórica na alimentação humana em países em desenvolvimento. No Brasil, o sorgo granífero é o principal substituto ao milho na formulação de rações para aves, suínos, bovinos e do segmento de pet food. Uma das grandes vantagens da cultura é sua tolerância à deficiência hídrica e solos com baixa fertilidade. Devido a estas características, o cultivo do sorgo tem se expandido durante a época da safrinha, período em que o volume e a frequência de chuvas costumam ser oscilantes e insuficientes. Na busca por cultivares mais adaptadas a estas condições, os programas de melhoramento de sorgo têm buscado novas combinações de híbridos com alto rendimento de grãos, altura de planta ideal para colheita mecanizada e precocidade. Diante deste cenário, os objetivos do trabalho foram: i) estimar a capacidade combinatória de linhagens de sorgo granífero, visando propor uma estratégia de melhoramento para desenvolvimento de novas linhagens macho-estéreis e linhagens restauradoras de fertilidade com potencial para confecção de híbridos com desempenho superior para os caracteres de interesse; ii) identificar híbridos que reúnam alta produtividade, precocidade, altura adequada à colheita e estabilidade fenotípica. Para tanto, 36 híbridos provenientes do cruzamento entre 12 linhagens de sorgo granífero (seis linhagens A x seis linhagens R) foram avaliados em experimentos conduzidos em Sinop, Mato Grosso, e em Sete Lagoas, Minas Gerais. Os caracteres avaliados foram: dias para o florescimento (DF), altura de plantas (AP) e produtividade de grãos (PROD). Para a análise dialélica, adotou-se o método 4 de Griffing (1962) adaptado a dialelos parciais. Para identificar os cruzamentos que menos contribuíram para a interação G x A foi realizada análise de Wricke (1962). Todas as análises foram realizadas com o software Genes. Cruzamentos múltiplos devem ser realizados para reunir os alelos favoráveis para os caracteres avaliados em novas linhagens restauradoras e macho- estéreis. Os híbridos 7, 9, 19 e 22 são os mais indicados para cultivo nos ambientes avaliados, pois possuem alta precocidade, porte adequado à colheita e alta produtividade de grãos, além de alta estabilidade fenotípica para estes caracteres. / Grain sorghum is considered the fifth most cultivated cereal in the world, being an important caloric source in human food in developing countries. In Brazil, grain sorghum is the main substitute for maize in feed formulation for poultry, pigs, cattle and pet food segment. One of the great crop advantages is its tolerance to water deficit and low fertility soils. Due to these characteristics, sorghum growing has expanded during the off-season, period in which the volume and frequency of rainfall are often oscillating and insufficient. In the search for cultivars better adapted to these conditions, sorghum breeding programs have sought new combinations of hybrids with high grain yield, ideal plant height to harvesting and earliness. Thus, the objectives of this study were: i) to estimate the combining ability of grain sorghum lines, aiming at proposing a breeding strategy for developing new male-sterile and fertility restorative lines with potential for obtaining hybrids with superior performance for the traits of interest; ii) to identify hybrids that meet high yield, earliness, adequate height to harvesting and phenotypic stability. Thirty-six hybrids from the crosses of 12 grain sorghum lines (six lines A x six lines R) were evaluated in experiments conducted in Sinop, Mato Grosso, and Sete Lagoas, Minas Gerais. The evaluated traits were: days to flowering (DF), plant height (PH) and grain yield (YIE). For the diallel analysis, the model proposed by Geraldi and Miranda Filho, adapted for partial diallel was adopted. To identify the crosses that contributed least to the G x E interaction, Wricke (1962) analysis was performed. All analyses were performed with Genes software. Multiple crosses should be performed to gather the favorable alleles for the traits evaluated in new restorative and male-sterile lines. Hybrids 7, 9, 19 and 22 are the most suitable for growing in the evaluated environments, since they have high earliness, adequate height to harvesting and high grain yield, as well as high phenotypic stability for these traits.

Peanut (Arachis hypogaea L.) is second major legume crop grown after soybean in the United States, and its productivity is often limited by drought stress. Drought negatively impacts the yield and quality of peanut. Drought stress in peanut causes an annual loss of approximately $520 million in the United States. Improving peanut yield under water deficit conditions is crucial for peanut growers to maintain their profitability in the market. To achieve this, it is essential to either breed or adopt already available drought tolerant cultivars that can produce higher yield under water deficit conditions. Therefore, the objectives of this research were to (1) evaluate five commercially available virginia and runner type peanut cultivars for pod yield stability using multilocation trials by studying G x E interaction across 13 environments including year, location, and irrigation regime. Linn and Binns, AMMI, Shukla, Wricke's, Finlay and Wilkinson stability models were used to determine pod yield stability. Bailey and Sullivan showed higher stability and adaptability across all stability indices whereas Wynne and TUFRunner presented high mean productivity with lesser stability across environments reflecting specific adaptation to just a few environments. Bailey and Sullivan are recommended for sustainable production across the growing region of Virginia and Carolinas. The second objective (2) was identification of drought tolerance related quantitative trait loci (QTL) and genetic markers to facilitate the development of drought tolerant cultivars. Three diverse recombinant inbred line (RIL) populations, derived from crossing lines N05006 x N04074FCT (Pop-1), line N05006 x Phillips, an old virginia-type cultivar (Pop-2), and lines N08086olJCT x PI 585005 (Pop-3) were phenotyped for the Normalized Difference Vegetation Index (NDVI), Canopy Temperature Depression (CTD), SPAD-meter relative chlorophyll content of the leaves (SPAD) and wilting for QTL mapping. Mapping identified 27 minor QTL on eight chromosomes for all physiological characteristics, i.e NDVI, CTD, SPAD and wilting, with logarithmic of odds values ranging from 2.5 to 38.5 and the phenotypic variance explained by these traits from 1.04 to 11.46 %. There were 4 loci on chromosome 2 associated with NDVI in Pop-1 and Pop-3, explaining 1.8 to 10.38% of the phenotypic variation. These genomic regions may be important resources in peanut breeding programs to improve drought tolerance. Further research is needed to increase the marker density in order to fine map the identified QTL and validate markers linked with these regions. / Doctor of Philosophy / Peanut is a multi million-dollar industry in the United States, but water limitations have a detrimental impact on yield, quality, and grower income. Drought along with aflatoxin contamination are two major challenges faced by U.S peanut industry. Annual losses to peanut caused by drought are around $520 million in the United States. Irrigation can alleviate water shortage in drought prone regions, but around 65% of peanut production in U.S is under rainfed condition, meaning that only rainfall can satisfy peanut crop water requirements. The most feasible and economical solution to peanut growers under these circumstances is to adopt drought tolerant varieties. In this research, our goal was to facilitate breeding drought tolerant cultivars through identification of molecular markers associated with drought tolerance and to identify already available drought tolerant peanut cultivars that could be a game changer for the producers. Therefore, the objectives of my research were to (1) evaluate in multiple environments five commercially available virginia and runner type peanut cultivars for pod yield stability and grade factors. In this study, we considered 13 environments, including 4 years, 4 locations, and 2 water regime. Statistical tools including Linn and Binns, AMMI, Shukla, Wricke's, and Finlay and Wilkinson were used to determine pod yield stability. These stability indices showed that Bailey and Sullivan are more stable and adaptable across different locations in terms of yield, whereas Wynne and TUFRunner presented high mean yield with lesser stability showing specific adaptation to only few environments. Based on stability analysis, Bailey and Sullivan are recommended for sustainable production across different growing region of Virginia and Carolinas. The second objective (2) was to identify drought tolerance related genomic regions using three mapping populations. Phenotyping and genotyping of three diverse recombinant inbred line (RIL) populations, derived from crossing lines N05006 x N04074FCT (Pop-1), lines N05006 x Phillips, an old virginia-type cultivar (Pop-2), and lines N08086olJCT x PI 585005 (Pop-3) were done to find quantitative trait loci (QTL) for drought related traits. These population were phenotyped for the Normalized Difference Vegetation Index (NDVI), Canopy Temperature Depression (CTD), SPAD-meter relative chlorophyll content of the leaves (SPAD) and wilting for QTL mapping. These surrogate traits are related to trait of interest for drought tolerance. NDVI is effective in predicting biomass and yield. Similarly, CTD is associated with transpiration efficiency and carbon dioxide assimilation. Mapping identified 27 minor QTL on eight chromosomes for all physiological characteristics, i.e NDVI, CTD, SPAD and wilting with logarithmic of odds values range from 2.5 to 38.5 and the phenotypic variance explained by these traits ranging from 1.04 to 11.46 %. There were 4 loci on chromosome 2 associated with NDVI in Pop-1 and Pop-3, explaining 1.8 to 10.38% of the phenotypic variation. These genomic regions may be important resources in peanut breeding programs to improve drought tolerance. Further research is needed to increase the marker density in order to fine map the identified QTL and validate markers linked with these regions.

Ce travail étudie les variétés pseudo-riemanniennes compactes localement homogènes à travers le prisme des (G,X)-structures, introduites par Thurston dans son programme de géométrisation. Nous commençons par présenter la problématique générale et discutons notamment du rapport entre la complétude géodésique de ces variétés et une autre notion de complétude propre aux (G,X)-structures. Nous donnons également dans le chapitre 1 une nouvelle preuve d’un théorème de Bromberg et Medina qui classifie les métriques lorentziennes invariantes à gauche sur SL(2,R) dont le flot géodésique est complet. Conjecturalement, toute (G,X)-structure pseudo-riemannienne sur une variété compacte est complète. Nous prouvons ici que cela est vrai pour certaines géométries, sous l’hypothèse que la (G,X)-structure est a priori kleinienne. On en déduit que, pour ces géométries, la complétude est une condition fermée. Lorsque X est un groupe de Lie de rang 1 muni de sa métrique de Killing, ce résultat complète un théorème de Guéritaud–Guichard–Kassel–Wienhard selon lequel la complétude est une condition ouverte. Nous nous tournons ensuite vers l’étude des représentations d’un groupe de surface à valeurs dans les isométries d’une variété riemannienne M complète simplement connexe de courbure sectionnelle inférieure à -1. Étant donnée une telle représentation ρ, nous montrons que l’ensemble des représentations fuchsiennes j telles qu’il existe une application (j,ρ)-équivariante et contractante de H2 dans M est un ouvert non vide et contractile de l’espace de Teichmüller (sauf lorsque ρ est elle-même fuchsienne). Ce résultat nous permet de décrire l’espace des métriques lorentziennes de courbure constante -1 sur un fibré en cercle au-dessus d’une surface compacte. Nous montrons que cet espace possède un nombre fini de composantes connexes classifiées par un invariant que nous appelons longueur de la fibre. Nous prouvons également que le volume total de ces métriques ne dépend que de la topologie du fibré et de la longueur de la fibre. / In this work, we study closed locally homogeneous pseudo-Riemannian manifolds through the notion of (G,X)-structure, introduced by Thurston in his geometrization program. We start by presenting the general problem. In particular, we discuss the link between geodesical completeness of those manifolds and another notion of completeness specific to (G,X)-structures. In chapter 1, we also give a new proof of a theorem by Bromberg and Medina which classifies left invariant Lorentz metrics on SL(2,R) that are geodesically complete. Conjecturally, every pseudo-riemannian (G,X)-structure on a closed manifold is complete. Here we prove that it holds for certain geometries, provided that the (G,X )-structure is a priori Kleinian . This implies that, for such geometries, completeness is a closed condition. When X is a Lie group of rank 1 handled with its Killing metric, this result complements a theorem of Guéritaud–Guichard–Kassel–Wienhard, acording to which completeness is an open condition. We then turn to the study of representations of surface groups into the isometry group of a complete simply connected Riemannian manifold M of curvature less than or equal to -1. Given such a representation ρ, we prove that the set of Fuchsian representations j for which there exists a (j,ρ)-equivariant contracting map from H2 to M is a non-empty open contractible subset of the Teichmüller space (unless ρ itself is Fuchsian). This result allows us to describe the space of Lorentz metrics of constant curvature -1 on a circle bundle over a closed surface. We show that this space has finitely many connected components, classified by an invariant that we call the length of the fiber. We also prove that the total volume of those metrics only depends on the topology of the bundle and on the length of the fiber.

Contrary to the predictions of numerous theoretical models, variation in partner quality continues to persist in mutualisms, including in the symbiosis between legumes and rhizobia. One potential explanation for the maintenance of this genetic diversity is genotype × genotype interactions, however it is unknown which genetic regions might underlie these interactions. To investigate this question, I performed a quantitative trait loci mapping experiment with two different rhizobium strains to locate potential regions of the genome influencing genotype × genotype interactions between the legume Medicago truncatula and its symbiont Sinorhizobium meliloti. I found no evidence for genotype × genotype or QTL × rhizobium interactions, however some of the QTLs colocalized with genes involved in the symbiosis signaling pathway, suggesting variation in these genes could potentially affect plant performance and fitness traits. These findings have important implications for the evolutionary interactions between legumes and rhizobia, and the genetic architecture of Medicago truncatula.

Contrary to the predictions of numerous theoretical models, variation in partner quality continues to persist in mutualisms, including in the symbiosis between legumes and rhizobia. One potential explanation for the maintenance of this genetic diversity is genotype × genotype interactions, however it is unknown which genetic regions might underlie these interactions. To investigate this question, I performed a quantitative trait loci mapping experiment with two different rhizobium strains to locate potential regions of the genome influencing genotype × genotype interactions between the legume Medicago truncatula and its symbiont Sinorhizobium meliloti. I found no evidence for genotype × genotype or QTL × rhizobium interactions, however some of the QTLs colocalized with genes involved in the symbiosis signaling pathway, suggesting variation in these genes could potentially affect plant performance and fitness traits. These findings have important implications for the evolutionary interactions between legumes and rhizobia, and the genetic architecture of Medicago truncatula.