A group W is said to have property FA_n if every action of W by isometries on an n-dimensional CAT(0) cell complex has a global fixed point. We construct a complex on which a Coxeter group W acts by cellular isometries without global fixed points, and show that under certain combinatorial conditions, complexes constructed in this way are CAT(0). We then construct several infinite classes of Coxeter groups which have property FA_2 but not property FA_3. / text

No description available.

Η παρούσα διατριβή αφορά στη μελέτη του συνόρου υπερβολικών δισδιάστατων πολυέδρων. Οι χώροι οι οποίοι μελετώνται κατασκευάζονται κολλώντας υπερβολικά τρίγωνα τα οποία έχουν 2 τουλάχιστον κορυφές στο άπειρο. Οι συγκολλήσεις γίνονται με ισομετρίες κατά μήκος των πλευρών των τριγώνων και οι χώροι οι οποίοι προκύπτουν εφοδιάζονται φυσιολογικά με μία γεωμετρία η οποία έχει ομοιότητες με την γεωμετρία των υπερβολικών πολλαπλοτήτων. Αρχικά μελετάμε τις βασικές ιδιότητες των δισδιάστατων ιδεωδών πολυέδρων και αποδεικνύουμε ότι: «Για κάθε δύο σημεία του συνόρου του καθολικού καλύμματος του χώρου που κατασκευάζουμε, υπάρχει άπειρο πλήθος υποχώρων του συνόρου ομοιομορφικών με το οι οποίοι περιέχουν τα σημεία αυτά». Στη συνέχεια, για μια ειδική κλάση πολυέδρων που κατασκευάζουμε κολλώντας με ισομετρίες κατά μήκος των πλευρών τους πεπερασμένα υπερβολικά τρίγωνα τα οποία έχουν δύο κορυφές στο άπειρο, αποδεικνύουμε επιπλέον ότι: «το σύνορο του καθολικού καλύμματος του χώρου που κατασκευάζουμε είναι τοπικά συνεκτικό κατά τόξα». Τέλος, στην τρίτη ενότητα δίδουμε μια τοπολογική περιγραφή του συνόρου των ιδεωδών πολυέδρων διάστασης 2. / The present work is related to the study of the visual boundary of hyperbolic two dimensional simplicial complexes. We construct (and study) spaces by gluing hyperbolic triangles with at least two vertices at infinity. We glue the triangles by isometries along their sides and we study the derived spaces. In the first chapter it is proved that for every two points in the visual boundary of the universal covering of a two dimensional ideal polyhedron, there is an infinity of paths joining them. In the second chapter, a class of hyperbolic two dimensional complexes X is defined. Is is shown that the limit set of the action of π1(X) on the universal covering of X, is equal to the visual boundary and also that the visual boundary is path connected and locally path connected. Finally, in the third chapter a kind of Sierpinski set is described which is homeomorphic to the visual boundary of certain ideal polyhedra.

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2017-04-05T14:15:45Z No. of bitstreams: 2 Dissertação - Mayara Vieira Santos - 2017.pdf: 4242091 bytes, checksum: e1114c1030f1c4a78d59b8f716e90e79 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-04-05T14:16:02Z (GMT) No. of bitstreams: 2 Dissertação - Mayara Vieira Santos - 2017.pdf: 4242091 bytes, checksum: e1114c1030f1c4a78d59b8f716e90e79 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-04-05T14:16:02Z (GMT). No. of bitstreams: 2 Dissertação - Mayara Vieira Santos - 2017.pdf: 4242091 bytes, checksum: e1114c1030f1c4a78d59b8f716e90e79 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2017-02-24 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Usually the inoculum used during the beginning of the harvest of ethanol production is constituted by the combination of two or more yeasts strains and in the end the most adapted one will predominate, either inoculated yeast or indigenous wild yeast. The proportion used in these industries are established empirically, of which little is known about the kinetic parameters and the influence that each yeast has on the production of ethanol and on the other metabolites. An experimental design from the blending design with Saccharomyces cerevisiae ATCC7754, S. cerevisiae CAT-1, S. cerevisiae PEDRA-2, S. cerevisiae MONASTRELL strains was proposed to understand how the interaction among the different blends occurs comparing with the ethanol, biomass, acetic acid, glycerol and biomass consumption. This study showed that the inherent characteristics to each yeast can influence the behavior of the kinetics parameters of the culture with two yeasts. It was verified that the combination among three yeasts presented similar metabolic behavior. From the blending design it was possible to elaborate mathematical models that predicts the ethanol, biomass, glycerol, acetic acid and residual sucrose amount in all four yeasts mixtures. It was also possible to identify that the mixture of CAT-1 and PEDRA-2 presented higher ethanol production when cultivated in a 1: 1 ratio, and also in the cultivation with the two yeasts (CAT-1 and PEDRA-2) to CAT-1 was higher in yeast. This research also presents the synthetic cane juice composition and the detail of growth kinetics, substrates consume and production of MONASTRELL yeast products that had not been studied until now. / Normalmente o inóculo utilizado durante o início da safra da produção de etanol é constituído da combinação de duas ou mais linhagem de leveduras e no final prevalece aquela que mais se adaptar, seja as leveduras inoculadas ou leveduras selvagens autóctones. Quanto as proporções utilizadas nas industrias essas são estabelecidas de forma empírica, dos quais sabe-se pouco sobre os parâmetros cinéticos e a influência que cada levedura acarreta sobre a produção do etanol e sobre os outros metabólitos. Um planejamento experimental a partir do delineamento de mistura com as cepas de Saccharomycescerevisiae ATCC7754, S. cerevisiae CAT-1, S. cerevisiae PEDRA-2, S. cerevisiae MONASTRELL foi proposto para entender como ocorre a interação entre as diferentes misturas comparando com os cultivos puros diante das respostas etanol, biomassa, ácido acético, glicerol e consumo de biomassa. Neste estudo mostrou que as características inerentes a cada levedura podem influenciar no comportamento dos parâmetros cinéticos do cultivo com duas leveduras. Verificou-se que a maioria das combinações entre três leveduras apresentam comportamento metabólico semelhante. A partir do delineamento de mistura pôde elaborar modelos matemáticos que predizem a quantidade de etanol, biomassa, glicerol, ácido acético e sacarose residual nas misturas das quatro leveduras. Conseguiu-se também identificar que o ensaio com a mistura de CAT-1 e PEDRA-2 apresentou maior produção de etanol na proporções de 1:1 da concentração de inóculo, e ainda neste cultivo a CAT-1 se sobressaiu em quantidade de leveduras. Esta pesquisa ainda apresenta a composição de caldo de cana-de-açúcar sintético e o detalhamento da cinética de crescimento, consumo de substrato e produção de produtos da levedura MONASTRELL que até então não tinham sido estudada.