Tesis sobre el tema "Ergodic and geometric group theory"
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Cannizzo, Jan. "Schreier Graphs and Ergodic Properties of Boundary Actions". Thesis, Université d'Ottawa / University of Ottawa, 2014. http://hdl.handle.net/10393/31444.
Texto completoLong, Yusen. "Diverse aspects of hyperbolic geometry and group dynamics". Electronic Thesis or Diss., université Paris-Saclay, 2024. http://www.theses.fr/2024UPASM016.
Texto completoThis thesis explores diverse topics related to hyperbolic geometry and group dynamics, aiming to investigate the interplay between geometry and group theory. It covers a wide range of mathematical disciplines, such as convex geometry, stochastic analysis, ergodic and geometric group theory, and low-dimensional topology, etc. As research outcomes, the hyperbolic geometry of infinite-dimensional convex bodies is thoroughly examined, and attempts are made to develop integral geometry in infinite dimensions from a perspective of stochastic analysis. The study of big mapping class groups, a current focus in low-dimensional topology and geometric group theory, is undertaken with a complete determination of their fixed-point on compacta property. The thesis also clarifies certain folklore theorems regarding the Gromov hyperbolic spaces and the dynamics of amenable groups on them. Last but not the least, the thesis studies the connectivity of the Gromov boundary of fine curve graphs, a combinatorial tool employed in the study of the homeomorphism groups of surfaces of finite type
Benson, Martin. "Topics in geometric group theory". Thesis, University of Nottingham, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.428957.
Texto completoWilliams, Benjamin Thomas. "Two topics in geometric group theory". Thesis, University of Southampton, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.323942.
Texto completoIsenrich, Claudio Llosa. "Kähler groups and Geometric Group Theory". Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:4a7ab097-4de5-4b72-8fd6-41ff8861ffae.
Texto completoAshdown, M. A. J. "Geometric algebra, group theory and theoretical physics". Thesis, University of Cambridge, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.596181.
Texto completoGill, Olivia Jo. "Geometric and homological methods in group theory : constructing small group resolutions". Thesis, London Metropolitan University, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.573402.
Texto completoJoubert, Paul. "Geometric actions of the absolute Galois group". Thesis, Stellenbosch : University of Stellenbosch, 2006. http://hdl.handle.net/10019.1/2508.
Texto completoThis thesis gives an introduction to some of the ideas originating from A. Grothendieck's 1984 manuscript Esquisse d'un programme. Most of these ideas are related to a new geometric approach to studying the absolute Galois group over the rationals by considering its action on certain geometric objects such as dessins d'enfants (called stick figures in this thesis) and the fundamental groups of certain moduli spaces of curves. I start by defining stick figures and explaining the connection between these innocent combinatorial objects and the absolute Galois group. I then proceed to give some background on moduli spaces. This involves describing how Teichmuller spaces and mapping class groups can be used to address the problem of counting the possible complex structures on a compact surface. In the last chapter I show how this relates to the absolute Galois group by giving an explicit description of the action of the absolute Galois group on the fundamental group of a particularly simple moduli space. I end by showing how this description was used by Y. Ihara to prove that the absolute Galois group is contained in the Grothendieck-Teichmuller group.
El-Mosalamy, Mohamed Soliman Hassan. "Applications of star complexes in group theory". Thesis, University of Glasgow, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.293464.
Texto completoFennessey, Eric James. "Some applications of geometric techniques in combinatorial group theory". Thesis, University of Glasgow, 1989. http://theses.gla.ac.uk/6159/.
Texto completoBergeron, Maxime. "On CAT(0) aspects of geometric group theory and some applications to geometric superrigidity". Thesis, McGill University, 2012. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=110571.
Texto completoDepuis leur popularisation par Gromov durant les années quatre-vingt, la théorie des espaces métriques à courbure bornée, dits CAT(0), fut à la base de grandes percées dans notre compréhension des groupes infinis. Survolant des constructions de la théorie géométrique des groupes, nous portons donc une attention particulière aux actions sur les espaces CAT(0) et commençcons notre traité par la construction de complexes CAT(0) obtenus en identifiant certaines faces isométriques d'ensembles de polyèdres convexes. Dans ce contexte, le critère du lien de Gromov nous permet de caractériser la courbure nonpositive globale de manière locale. Combinant ces idées à certaines techniques de la théorie des noeuds, nous démontrons un théorème de Wise reliant tout groupe fondamental du complément d'un entrelac alternants à un complexe de courbure nonpositive. Nous relatons aussi une construction similaire de Wise permettant de relier tout groupe présenté de manière finie au groupe fondamental d'un complexe à courbure nonpositive. Outre ces constructions concrètes, nous utilisons les tours de relèvement d'applications combinatoires afin de démontrer un théorème abstrait de Bridson et Haefliger concernant les sous-groupes de groupes fondamentaux de complexes à courbure non-positive. Ayant établi la structure des espaces CAT(0), nous passons en second lieu à la classification de leurs isométries et de leurs extensions à la bordification de ces espaces. L'approche combinatoire est d'une aide particulière lorsque nous prouvons le résultat de Haglund concernant la semi-simplicité d'isométries de complexes cubiques et offre un contraste par rapport à un résultat analogue de Brisdon dans le contexte des complexes polyhédraux. Finalement, en faisant usage de la théorie des applications harmoniques généralisées, nous démontrons le résultat de superrigidité de Monod, Gelander, Karlsson et Margulis pour les actions réduites sans point fixe sur les espaces métriques CAT(0) complets de réseaux uniformes et irréductibles dans des groupes de rang supérieur localement compacts engendrés par un ensemble de générateurs compact.
Jarrett, Kieran. "Non-singular actions of countable groups". Thesis, University of Bath, 2018. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.761021.
Texto completoBavuma, Yanga. "Some combinatorial aspects in algebraic topology and geometric group theory". Master's thesis, University of Cape Town, 2018. http://hdl.handle.net/11427/29763.
Texto completoDavidson, Peter John. "Geometric methods in the study of Pride groups and relative presentations". Thesis, Connect to e-thesis, 2008. http://theses.gla.ac.uk/230/.
Texto completoPh.D. thesis submitted to the Faculty of Information and Mathematical Sciences, Department of Mathematics, University of Glasgow, 2008. Includes bibliographical references. Print version also available.
Sathaye, Bakul Sathaye. "Obstructions to Riemannian smoothings of locally CAT(0) manifolds". The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1531416481628579.
Texto completoAtanasov, Risto. "Groups of geometric dimension 2". Diss., Online access via UMI:, 2007.
Buscar texto completoCotton-Barratt, Owen. "Geometric and profinite properties of groups". Thesis, University of Oxford, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.572875.
Texto completoGenevois, Anthony. "Cubical-like geometry of quasi-median graphs and applications to geometric group theory". Thesis, Aix-Marseille, 2017. http://www.theses.fr/2017AIXM0569/document.
Texto completoThe class of quasi-median graphs is a generalisation of median graphs, or equivalently of CAT(0) cube complexes. The purpose of this thesis is to introduce these graphs in geometric group theory. In the first part of our work, we extend the definition of hyperplanes from CAT(0) cube complexes, and we show that the geometry of a quasi-median graph essentially reduces to the combinatorics of its hyperplanes. In the second part, we exploit the specific structure of the hyperplanes to state combination results. The main idea is that if a group acts in a suitable way on a quasi-median graph so that clique-stabilisers satisfy some non-positively curved property P, then the whole group must satisfy P as well. The properties we are interested in are mainly (relative) hyperbolicity, (equivariant) lp-compressions, CAT(0)-ness and cubicality. In the third part, we apply our general criteria to several classes of groups, including graph products, Guba and Sapir's diagram products, some wreath products, and some graphs of groups. Graph products are our most natural examples, where the link between the group and its quasi-median graph is particularly strong and explicit; in particular, we are able to determine precisely when a graph product is relatively hyperbolic
Awang, Jennifer S. "Dots and lines : geometric semigroup theory and finite presentability". Thesis, University of St Andrews, 2015. http://hdl.handle.net/10023/6923.
Texto completoGielen, Steffen C. M. "Geometric aspects of gauge and spacetime symmetries". Thesis, University of Cambridge, 2011. https://www.repository.cam.ac.uk/handle/1810/240578.
Texto completoSisto, Alessandro. "Geometric and probabilistic aspects of groups with hyperbolic features". Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:bcf456c4-eef0-4fe8-bb7d-8b15f9cf7b18.
Texto completoSercombe, Damian. "A family of uniform lattices acting on a Davis complex with a non-discrete set of covolumes". Thesis, The University of Sydney, 2015. http://hdl.handle.net/2123/16026.
Texto completoBarrett, Benjamin James. "Detecting topological properties of boundaries of hyperbolic groups". Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/285572.
Texto completoSolomyak, Margarita. "Essential spanning forests and electric networks in groups /". Thesis, Connect to this title online; UW restricted, 1997. http://hdl.handle.net/1773/5767.
Texto completoKuckuck, Benno. "Finiteness properties of fibre products". Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:a9624d17-9d11-4bd0-8c46-78cbba73469c.
Texto completoCornwell, Christopher R. "On the Combinatorics of Certain Garside Semigroups". Diss., CLICK HERE for online access, 2006. http://contentdm.lib.byu.edu/ETD/image/etd1381.pdf.
Texto completoCannas, Sonia. "Geometric representation and algebraic formalization of musical structures". Thesis, Strasbourg, 2018. http://www.theses.fr/2018STRAD047/document.
Texto completoThis thesis presents a generalizations of the neo-Riemannian PLR-group, that acts on the set of 24 major and minor triads. The work begins with a reconstruction on the history of the Tonnetz, a graph associated with the three transformations that generate the PLR-group. The thesis presents two generalizations of the PLR-group for seventh chords. The first one acts on the set of dominant, minor, semi-diminished, major and diminished sevenths, the second one also includes minor major, augmented major, augmented, dominant seventh flat five. We considered the most parsimonious operations exchanging two types of sevenths, moving a single note by a semitone or a whole tone. We also classified the most parsimonious transformations among the 4 types of triads (major, minor,augmented and diminished) and studied the group generated by them. Finally, we have introduced a general approach to define parsimonious operations between sevenths and triads, but also the operations already known between triads and those between sevenths
Woodruff, Benjamin M. "Statistical Properties of Thompson's Group and Random Pseudo Manifolds". Diss., CLICK HERE for online access, 2005. http://contentdm.lib.byu.edu/ETD/image/etd854.pdf.
Texto completoCarette, Mathieu. "The automorphism group of accessible groups and the rank of Coxeter groups". Doctoral thesis, Universite Libre de Bruxelles, 2009. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210261.
Texto completoVia la théorie de Bass-Serre, un groupe agissant sur un arbre est doté d'une structure algébrique particulière, généralisant produits amalgamés et extensions HNN. Le groupe est en fait déterminé par certaines données combinatoires découlant de cette action, appelées graphes de groupes.
Un cas particulier de cette situation est celle d'un produit libre. Une présentation du groupe d'automorphisme d'un produit libre d'un nombre fini de groupes librement indécomposables en termes de présentation des facteurs et de leurs groupes d'automorphismes a été donnée par Fouxe-Rabinovich. Il découle de son travail que si les facteurs et leurs groupes d'automorphismes sont de présentation finie, alors le groupe d'automorphisme du produit libre est de présentation finie. Une première partie de cette thèse donne une nouvelle preuve de ce résultat, se basant sur le langage des actions de groupes sur les arbres.
Un groupe accessible est un groupe de type fini déterminé par un graphe de groupe fini dont les groupes d'arêtes sont finis et les groupes de sommets ont au plus un bout, c'est-à-dire qu'ils ne se décomposent pas en produit amalgamé ni en extension HNN sur un groupe fini. L'étude du groupe d'automorphisme d'un groupe accessible est ramenée à l'étude de groupes d'automorphismes de produits libres, de groupes de twists de Dehn et de groupes d'automorphismes relatifs des groupes de sommets. En particulier, on déduit un critère naturel pour que le groupe d'automorphismes d'un groupe accessible soit de présentation finie, et on donne une caractérisation des groupes accessibles dont le groupe d'automorphisme externe est fini. Appliqués aux groupes hyperboliques de Gromov, ces résultats permettent d'affirmer que le groupe d'automorphismes d'un groupe hyperbolique est de présentation finie, et donnent une caractérisation précise des groupes hyperboliques dont le groupe d'automorphisme externe est fini.
Enfin, on étudie le rang des groupes de Coxeter, c'est-à-dire le cardinal minimal d'un ensemble générateur pour un groupe de Coxeter donné. Plus précisément, on montre que si les composantes de la matrice de Coxeter déterminant un groupe de Coxeter sont suffisamment grandes, alors l'ensemble générateur standard est de cardinal minimal parmi tous les ensembles générateurs.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished
Gardam, Giles. "Encoding and detecting properties in finitely presented groups". Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:0c8a7009-7e04-4f66-911b-298ad87061fb.
Texto completoBounds, Jordan. "On the quasi-isometric rigidity of a class of right-angled Coxeter groups". Bowling Green State University / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1561561078356503.
Texto completoLynch, Keith. "On triangles and quadrilaterals of groups". Diss., Virginia Tech, 1995. http://hdl.handle.net/10919/38574.
Texto completoPh. D.
Sale, Andrew W. "The length of conjugators in solvable groups and lattices of semisimple Lie groups". Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:ea21dab2-2da1-406a-bd4f-5457ab02a011.
Texto completoLima, Francismar Ferreira 1985. "Pontos fixos por grupos finitos agindo sobre grupos solúveis de tipo FP infinito". [s.n.], 2013. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306924.
Texto completoDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
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Resumo: O resumo poderá ser visualizado no texto completo da tese digital
Abstract: The complete Abstract is available with the full electronic document.
Mestrado
Matematica
Mestre em Matemática
Shim, Sangho. "Large scale group network optimization". Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/31737.
Texto completoCommittee Chair: Ellis L. Johnson; Committee Member: Brady Hunsaker; Committee Member: George Nemhauser; Committee Member: Jozef Siran; Committee Member: Shabbir Ahmed; Committee Member: William Cook. Part of the SMARTech Electronic Thesis and Dissertation Collection.
Kelvey, Robert J. Kelvey. "Properties of groups acting on Twin-Trees and Chabauty space". Bowling Green State University / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1479423366082688.
Texto completoDisarlo, Valentina. "Combinatorial methods in Teichmüller theory". Doctoral thesis, Scuola Normale Superiore, 2013. http://hdl.handle.net/11384/85687.
Texto completoAlmeida, Kisnney Emiliano de 1984. "Sobre os sigma-invariantes unidimensionais de grupos de Artin". [s.n.], 2012. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306925.
Texto completoTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica
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Resumo: A teoria de ?-invariantes surgiu do trabalho de Bieri e Strebel, que definiram o primeiro ?-invariante, apenas para grupos metabelianos, e o usaram para descrever os grupos metabelianos finitamente gerados [BiSt]. Posteriormente, foram definidos os ?m-invariantes homotópicos e homológicos de grupos finitamente gerados arbitrários [BiNSt]. Estes são certos subconjuntos da esfera de caracteres profundamente relacionados às propriedades de finitude Fm e FPm, respectivamente. Os grupos de Artin formam uma grande classe de grupos, cada um associado a um grafo rotulado, que inclui algumas subclasses importantes, como "Braid groups" e "Rightangled Artin groups"...Observação: O resumo, na íntegra, poderá ser visualizado no texto completo da tese digital
Abstract: The ?-invariants theory arose from the work of Bieri and Strebel, who defined the first ?-invariant, for metabelian groups only, and used it to describe the finitely presented metabelian groups [BiSt]. Later on, the homotopical and homological ?m-invariants of arbitrary finitely generated groups were defined [BiRe]. These are certain subsets of the sphere of characters deeply related to the finiteness properties Fm and FPm, respectively. The Artin groups form a large class of groups, each one associated to a labeled graph, that includes some important subclasses, as Braid groups and Right-angled Artin groups...Note: The complete abstract is available with the full electronic document
Doutorado
Matematica
Doutor em Matemática
Yang, Ruotao. "Twisted Whittaker category on affine flags and category of representations of mixed quantum group". Electronic Thesis or Diss., Université de Lorraine, 2020. http://www.theses.fr/2020LORR0064.
Texto completoSuppose that G is a reductive group. We have the geometric Satake equivalence which identifies Sph (G), the perverse G (O) equivalent D-modules on affine grassmannin as the category of finite dimensional representation of H, the Langlands dual group of G. We note that: Whit(Gr) = Sph(G). Here, Whit (Gr) is the module category D (N (K), \ chi) -equivalent on Gr. Now, the category of representation admits a deformation by the category of representations of quantum group. On the Whittaker side, we can consider the twisted D-modules on affine grassmannin. This is the fundamental local equivalence: Whit_q (Gr) = Rep_q (H) . Recently, D. Gaitsgory proposed its ramified version. We consider the affine flags instead of the affine grassmannians. In this case, we have to replace the category of quantum group representations with another category, the category of mixed quantum group representations. Whit_q (Fl) = Rep_q ^ {mix} (H) . We prove that the category of twisted Whittaker D-modules on the affine flags and the category of representations of the mixed quantum group are equivalent
Disarlo, Valentina. "Combinatorial methods in Teichmüller theory". Phd thesis, Université de Strasbourg, 2013. http://tel.archives-ouvertes.fr/tel-00875029.
Texto completoMaillot, Sylvain. "Quasi-isométries, groupes de surfaces et orbifolds fibrés de Seifert". Phd thesis, Université Paul Sabatier - Toulouse III, 2000. http://tel.archives-ouvertes.fr/tel-00001342.
Texto completoCamelo, Botero Miguel Hernando. "A geometric routing scheme in word-metric spaces for data networks". Doctoral thesis, Universitat de Girona, 2014. http://hdl.handle.net/10803/283749.
Texto completoEste trabajo de investigación explora el uso de esquemas de Enrutamiento Geométrico Greedy (Greedy Geometric Routing o GGR) para resolver el problema de escalabilidad de los sistemas de encaminamiento de redes tipo Internet y de varias arquitecturas para Centros de Datos (Data Centers o DCs). Nosotros proponemos un nuevo y simple método de incrustación (embedding) de cualquier grafo finito y conectado en un espacio métrico de palabras (Word-Metric space), es decir, un espacio métrico generado por grupos algebraicos. Luego, construidos sobre esta incrustación, proponemos tres esquemas de GGR y derivamos los límites superiores teóricos de sus tablas de encaminamiento (Routing Table o RT), las etiquetas de los vértices y el stretch. El primer esquema trabaja sobre cualquier tipo de grafo y los otros dos son especializados para topologías tipo Internet y varias familias de arquitecturas de DCs
D'Andrea, Joy. "Fundamental Transversals on the Complexes of Polyhedra". Scholar Commons, 2011. http://scholarcommons.usf.edu/etd/3746.
Texto completoSilva, Leonardo de Amorin e. 1980. "Grupos abelianos-por-(nilpotentes de classe 2)". [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306919.
Texto completoTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
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Resumo: Nesta tese consideramos uma extensão cindida G de um grupo abeliano A por um grupo nilpotente (de classe 2) Q e provamos dois resultados. Primeiro, se Q age nilpotentemente sobre A e G tem tipo FP2, calculamos o sigma invariante de G em dimensão 2. Segundo, se G tem tipo FP4, mostramos que cada quociente de G tem tipo FP4
Abstract: In this thesis we consider a split extension G of an abelian group A by a nilpotent group (class 2) Q and prove two results. First, if Q acts nilpotently on A and G has type FP2, compute the sigma invariant of G in dimension 2. Second, if G has type FP4, we show that every quotient G has type FP4
Doutorado
Matematica
Doutora em Matemática
Nicol, Andrew. "Quasi-isometries of graph manifolds do not preserve non-positive curvature". The Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1405894640.
Texto completoDufloux, Laurent. "Dimension de Hausdorff des ensembles limites". Thesis, Sorbonne Paris Cité, 2015. http://www.theses.fr/2015USPCD022/document.
Texto completoLet G be the group SO° (1,n) (n ≥ 3) or PU(1, n) (n ≥ 2) and fix some Iwasawa decomposition G = KAN. Let ɼ be a discrete subgroup of G.We assume that ɼ is Zariski-dense with finite Bowen-Margulis-Sullivan measure. When G = SO°(1,n), we investigate the geometry of the Bowen-Margulis-Sullivan measure elong connected closed subgroups of N. This is related to the Mohammadi-Oh dichotomy. We then prove deterministic results on the dimension of projections of Patterson-Sullivan measure. When G = PU(1,n), we relate the geometry of Bowen-Margulis-Sullivan measure along the center of Heisenberg group to the problem of computing the Hausdorff dimension of the limit set with respect to the spherical metric on the boudary. We construct some Schottky subgroups for wich we are able to compute this dimension
Petersen, Willis L. "The Lie Symmetries of a Few Classes of Harmonic Functions". Diss., CLICK HERE for online access, 2005. http://contentdm.lib.byu.edu/ETD/image/etd837.pdf.
Texto completoBouette, Margot. "Sur la croissance des automorphismes des groupes de Baumslag-Soliltar". Thesis, Rennes 1, 2016. http://www.theses.fr/2016REN1S053/document.
Texto completoA Baumslag-Solitar group is a group given by the group presentation, for p and q non-zero integers. For each Baumslag-Solitar group we consider a deformation space D p, q which is analogue of Culler-Vogtmann's Outer Space. The action of Aut(BS(p, q)) on D p, q induces an action of the outer automorphism group Out(BS(pq)). We will focus on the case where p divides q. Firstly, we will show that every automorphism of BS(p,pn) is reducible which means that we can find a BS(p,pn)-tree T and a map that leaves a certain type of subforest invariant. This result leads us to introduce a new deformation space and a classification of the automorphisms of BS(p,pn) in three types : elliptic, parabolic or hyperbolic. Using this classification, we will show that the growth of every automorphism of BS(p,pn) is exponential or polynomial
Bouljihad, Mohamed. "Propriété (T) de Kazhdan relative à l'espace". Thesis, Lyon, 2016. http://www.theses.fr/2016LYSEN010/document.
Texto completoThe purpose of this thesis is to study the Kazhdan's property (T) relative to the space (also called rigidity in the sense of Popa) of probability measure preserving actions of countable groups on standard probability measure spaces (p.m.p.).This last decade, some problems in the theory of ergodic theory and von Neumann algebras were solved using the property (T) relative to the space. However, the theoretical aspects of its study remain largely mysterious. An open question asks which groups admit a p.m.p. free and ergodic action which has the property (T) relative to the space. We show in this dissertation that every finitely-generated non-amenable linear groups over a field of characteristic zero admits a p.m.p. ergodic action which has this property. If this group has trivial solvable radical, we prove that these actions can be chosen to be free.In order to obtain these results, we start by investigating natural questions concerning the stability of the property (T) relative to the space through standard constructions : products, restriction, co-induction, induction. Then, we give a criterion for the property (T) relative to the space to hold in the case of p.m.p. actions on homogeneous space G/ Λ of a p-adic Lie group for a countable subgroup Γ of affine transformations of G stabilizing the lattice Λ. The action of Γ on G/Λ has the property (T) relative to the space if and only if the induced action of Γ on the projective space of the Lie algebra of G admits no invariant probability measure.Moreover, we study the case of actions by automorphims on nilvarietes defined by finite graphs
Vittone, Davide. "Submanifolds in Carnot groups". Doctoral thesis, Scuola Normale Superiore, 2006. http://hdl.handle.net/11384/85698.
Texto completo