Thesis--Bonn. / Extra t.p. with thesis statement inserted. Includes bibliographical references.

Thesis (doctoral)--Bonn, 1997. / Includes bibliographical references (p. 93-95).

Thesis (doctoral)--Bonn, 1997. / Vita. Includes bibliographical references (p. 167-168).

Thesis (Ph.D.) -- University of Texas Southwestern Medical Center at Dallas, 2005. / Not embargoed. Vita. Bibliography: 182-209.

Thesis (Ph. D.)--University of Washington, 2005. / Vita. Includes bibliographical references (p. 83-102).

In this thesis we prove homological stability for both general linear groups of modules over a ring with finite stable rank and unitary groups of quadratic modules over a ring with finite unitary stable rank. In particular, we do not assume the modules and quadratic modules to be well-behaved in any sense: for example, the quadratic form may be singular. This extends results by van der Kallen and Mirzaii--van der Kallen respectively. Combining these results with the machinery introduced by Galatius--Randal-Williams to prove homological stability for moduli spaces of simply-connected manifolds of dimension $2n \geq 6$, we get an extension of their result to the case of virtually polycyclic fundamental groups. We also prove the corresponding result for manifolds equipped with tangential structures. A result on the stable homology groups of moduli spaces of manifolds by Galatius--Randal-Williams enables us to make new computations using our homological stability results. In particular, we compute the abelianisation of the mapping class groups of certain $6$-dimensional manifolds. The first computation considers a manifold built from $\mathbb{R} P^6$ which involves a partial computation of the Adams spectral sequence of the spectrum ${MT}$Pin$^{-}(6)$. For the second computation we consider Spin $6$-manifolds with $\pi_1 \cong \mathbb{Z} / 2^k \mathbb{Z}$ and $\pi_2 = 0$, where the main new ingredient is an~analysis of the Atiyah--Hirzebruch spectral sequence for $MT\mathrm{Spin}(6) \wedge \Sigma^{\infty} B\mathbb{Z}/2^k\mathbb{Z}_+$. Finally, we consider the similar manifolds with more general fundamental groups $G$, where $K_1(\mathbb{Q}[G^{\mathrm{ab}}])$ plays a role.

vii, 54 p. : ill. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. / We investigate the existence of a stable homotopy category (SHC) associated to the category of p -complete abelian groups [Special characters omitted]. First we examine [Special characters omitted] and prove [Special characters omitted] satisfies all but one of the axioms of an abelian category. The connections between an SHC and homology functors are then exploited to draw conclusions about possible SHC structures for [Special characters omitted]. In particular, let [Special characters omitted] denote the category whose objects are chain complexes of [Special characters omitted] and morphisms are chain homotopy classes of maps. We show that any homology functor from any subcategory of [Special characters omitted] containing the p-adic integers and satisfying the axioms of an SHC will not agree with standard homology on free, finitely generated (as modules over the p -adic integers) chain complexes. Explicit examples of common functors are included to highlight troubles that arrise when working with [Special characters omitted]. We make some first attempts at classifying small objects in [Special characters omitted]. / Committee in charge: Hal Sadofsky, Chairperson, Mathematics; Boris Botvinnik, Member, Mathematics; Daniel Dugger, Member, Mathematics; Sergey Yuzvinsky, Member, Mathematics; Elizabeth Reis, Outside Member, Womens and Gender Studies

Submitted by Pablo Gonzalez Pagotto null (pgp_2008@hotmail.com) on 2016-09-28T16:16:44Z No. of bitstreams: 1 final.pdf: 1327249 bytes, checksum: 26bc65e3566fd3813a93f271a02744c1 (MD5) / Approved for entry into archive by Ana Paula Grisoto (grisotoana@reitoria.unesp.br) on 2016-09-30T14:43:09Z (GMT) No. of bitstreams: 1 pagotto_pg_me_sjrp.pdf: 1327249 bytes, checksum: 26bc65e3566fd3813a93f271a02744c1 (MD5) / Made available in DSpace on 2016-09-30T14:43:09Z (GMT). No. of bitstreams: 1 pagotto_pg_me_sjrp.pdf: 1327249 bytes, checksum: 26bc65e3566fd3813a93f271a02744c1 (MD5) Previous issue date: 2016-08-30 / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / O objetivo principal deste trabalho é apresentar um estudo sobre Homologia de Espaços Fibrados, baseado no livro Elements of Homotopy Theory de G.W.Whitehead. O conceito de fibração apareceu em torno de 1930 e pode ser visto como uma extensão da teoria de fibrados. Existe uma sequência exata longa que relaciona os grupos de homotopia dos espaços base, total e da fibra de uma fibração. Porém, relacionar os grupos de homologia desses espaços é uma tarefa mais complicada. O caso geral é feito utilizando sequências espectrais. Porém, há casos particulares em que podemos obter relações sem utilizar a maquinaria das sequências espectrais. / The main goal of this work is to present a study on Homology of Fibre Spaces, based on the book of G.W. Whitehead: ``Elements of Homotopy Theory''. The concept of fibration appeared around 1930 and can be seen as an extension of the theory of bundles. There is a long exact sequence that relates the homotopy groups of the total, base and fiber spaces of a fibration. However, relating the homology groups of such spaces is more complicated. The general case is obtained using spectral sequences. Nevertheless there are particular cases where one can obtain such relations without the need of the machinery of spectral sequences. / FAPESP: 2013/22249-0

O conceito de homologia similaridade entre partes com ancestralidade comum é um dos mais importantes conceitos dentro das análises evolutivas. Desde a sua origem, muitas definições que diferem na definição e na aplicação foram propostas. A presente dissertação tem como objetivo reconstruir a história da homologia para esclarecer teoricamente os debates modernos. Após esta historiografia, foi feita uma análise filomemética dos principais autores que discutiram a teoria e a prática do conceito. E, por último, foi feita uma discussão teórica do papel da homologia dentro da sistemática filogenética, abordando as principais discussões atuais. Os resultados demonstram que é possível esclarecer algumas discussões através da análise histórica do conceito sob a perspectiva da teoria da evolução. A análise filomemética reconstruiu os grupos de autores de acordo com suas escolas e propostas sobre a homologia. A análise teórica do conceito na metodologia filogenética evidencia que o conceito de homologia é equivalente ao conceito de sinapomorfia e uma nova visão sobre a relação de ausências, homoplasias e homologias é proposta. A discussão sobre as nomenclaturas e definição do conceito de homologia demonstra que as terminologias homologia primária e secundária são as melhores propostas para representar a relação da origem e legitimação de homólogos. Uma crítica às análises filomeméticas conceituais é feita. / The concept of homology similarity between parts due to common ancestrality is one of the most important concept in evolutionary analysis. Since it origin, many definitions which differ on definition and application were proposed. This dissertation has as the main goal reconstruct the history of homology to clarify theoretically the modern debates. After this historiography, was made a phylomemetic analysis of main authors that discussed the theory and pratics of homology concept. Lastly, was made a discussion on the importance of the role of homology in phylogenetic systematics, approaching actual discussions. The results support that is possible to clarify some discussions through historical analysis of this concept with an evolutionary background. The phylomemetic analysis reconstruct groups of author accordingly to their methodological schools and propositions. The historical analysis of the concept in phylogenetic analysis evidence that homology concept is equivalent to synapomorphy and a new look into the relation of absence, homoplasy and homology is proposed. The discussion on nomenclatures and definition of the concept of homology support that primary and secondary homology are the best proposition to represent the relation of origin and legitimation of homologs. A criticism to phylomemetic analysis is pointed.

Submitted by Caroline Falcao (caroline.rfalcao@ufpe.br) on 2017-04-10T16:55:55Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) 2012-Dissertação-TyagoEufrásioSouza.pdf: 1735075 bytes, checksum: 71d298cc88578885aa679bda01ec12e1 (MD5) / Made available in DSpace on 2017-04-10T16:55:55Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) 2012-Dissertação-TyagoEufrásioSouza.pdf: 1735075 bytes, checksum: 71d298cc88578885aa679bda01ec12e1 (MD5) Previous issue date: 2012-02-29 / As espécies de gafanhotos Ommexecha virens(Ommexechidae),Xyleus discoideus angulatus,Tropidacris collaris(Romaleidae) eSchistocerca pallens(Acrididae)ocorrem na região do Nordeste do Brasil. Apresentam seus cariótipos simétricos com número cromossômico, 2n=23 (X0, machos) e 2n=24 (XX, fêmeas), porém T. collaris, S.pallense X.d.angulatus apresentam os cromossomos com morfologia acrocêntrica, enquanto que O. virens apresenta o par cromossômico G1submetacêntrico. Variaçõesrítmicasnocomportamentoapresentadaspordiversosorganismossão pertencentes ao ciclo circadiano.Com o uso da técnica de Hibridização in situ Permanente (PISH), foi mapeada a posição do gene de cópia única Per, um dos genes do relógio circadiano,em cromossomos meióticos das espécies O. virens,X.d.angulatus,T. collariseS.pallens.Os cromossomos meióticos destas espécies foram obtidos através da técnica clássica de esmagamento de folículos testiculares. As sondas utilizadas foram obtidas de plasmídeos carregando fragmentos do gene Per originários do genoma do drosofilídioZaprionus indianus. Após a hibridizaçãoin situ, o material foi fotografado usando contraste de fase. Nasquatroespéciesde gafanhotos citadas anteriormente, o gene Perfoi mapeado no maior par autossômico, G1.Analisados conjuntamente os resultados de mapeamento do genePer nestasespéciescom a localização de outros genes de cópia única e de cópia repetitiva, observa-se uma localização preferencial dos genes decópia única nos pares autossômicos grandes e, genes de cópia repetitiva, nos pares médios e pequenos. Estesresultadostambémapontam paraumaconservação molecular deste gene nos Orthoptera, como observado em Dípterae Lepdoptera; possívelmente a conservaçãona localização cromossômicasejaum reflexodaconservaçãomolecular.Localizações cromossômicas dediversosgenes constitutivos em representantes das famílias Ommexechidae, Romaleidae e Acrididaesão informações relevantes para o entendimento das relações evolutivas entre estesgafanhotos, além disso,fornecemmarcadores para o sequenciamento do genoma destas espécies. / The species of grasshoppers Ommexecha virens(Ommexechidae) Xyleus discoideus angulatus, Tropidacris collaris(Romaleidae) and Schistocerca pallens(Acrididae) occur in the Northeast region of Brazil. Present theirsymmetricalkaryotypeswithchromosome numbers, 2n = 23 (X0, males) and 2n = 24 (XX, females), butT. collaris, S. pallensand X. d. angulatuspresent the acrocentric chromosome morphology, while O. virensshows the submetacentric L1chromosome pair.Rhythmic variationsin behaviorpresented byvarious organimsare belongingto the circadian cycle.Using the technique of Permanent insituhybridization (PISH), has mapped the position of thesingle-copy genePer, one of the clock genes, in meiotic chromosomes of the species O. virens, T. collaris, S. pallensand X. d. angulatus. The meiotic chromosomes of these species were obtained by the classical technique of crushing testicular follicles. The probe used was obtained from plasmids carrying the gene Perfragments originating from the genome of drosofilid Zaprionusindianus. After in situ hybridization, the material was photographed using phase contrast. In thegrasshoppersspecies mentioned above, the Pergene was mapped in largest autosomal pair, L1. Taken together the results of Pergene mapping in these species with the location of other single-copy genes and repetitive copy, there is a preferential localization of single copy genes in large autosomal pairs and copy repetitive genes, the couplepairsand small. These results also point to a molecular conservation of this gene in the Orthoptera, as observed in Diptera and Lepdoptera, possible conservation in chromosomal location is a reflection of molecular conservation. Chromosomal locations of severalconstituentgenes in representatives of the families constituting Ommexechidae, RomaleidaeandAcrididae are relevant information for understanding the evolutionary relationships in the locusts, and provides markers for mapping the genome of these species.