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# Documents  20F65 | enregistrements trouvés : 86

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## The visual boundary of hyperbolic free-by-cyclic groups Stark, Emily | CIRM H

Post-edited

Research talks;Geometry;Topology

Given an automorphism of the free group, we consider the mapping torus defined with respect to the automorphism. If the automorphism is atoroidal, then the resulting free-by-cyclic group is hyperbolic by work of Brinkmann. In addition, if the automorphism is fully irreducible, then work of Kapovich-Kleiner proves the boundary of the group is homeomorphic to the Menger curve. However, their proof is very general and gives no tools to further study the boundary and large-scale geometry of these groups. In this talk, I will explain how to construct explicit embeddings of non-planar graphs into the boundary of these groups whenever the group is hyperbolic. Along the way, I will illustrate how our methods distinguish free-by-cyclic groups which are the fundamental group of a 3-manifold. This is joint work with Yael Algom-Kfir and Arnaud Hilion. Given an automorphism of the free group, we consider the mapping torus defined with respect to the automorphism. If the automorphism is atoroidal, then the resulting free-by-cyclic group is hyperbolic by work of Brinkmann. In addition, if the automorphism is fully irreducible, then work of Kapovich-Kleiner proves the boundary of the group is homeomorphic to the Menger curve. However, their proof is very general and gives no tools to further ...

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## On subgroups of R. Thompson's group $F$ Sapir, Mark | CIRM H

Post-edited

Research talks;Algebra

We provide two ways to show that the R. Thompson group $F$ has maximal subgroups of infinite index which do not fix any number in the unit interval under the natural action of $F$ on $(0,1)$, thus solving a problem by D. Savchuk. The first way employs Jones' subgroup of the R. Thompson group $F$ and leads to an explicit finitely generated example. The second way employs directed 2-complexes and 2-dimensional analogs of Stallings' core graphs, and gives many implicit examples. We also show that $F$ has a decreasing sequence of finitely generated subgroups $F>H_1>H_2>...$ such that $\cap H_i={1}$ and for every $i$ there exist only finitely many subgroups of $F$ containing $H_i$. We provide two ways to show that the R. Thompson group $F$ has maximal subgroups of infinite index which do not fix any number in the unit interval under the natural action of $F$ on $(0,1)$, thus solving a problem by D. Savchuk. The first way employs Jones' subgroup of the R. Thompson group $F$ and leads to an explicit finitely generated example. The second way employs directed 2-complexes and 2-dimensional analogs of Stallings' core graphs, ...

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## Coarse dimension reduction Naor, Assaf | CIRM H

Post-edited

Research talks;Analysis and its Applications

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## Endomorphisms, train track maps, and fully irreducible monodromies Kapovich, Ilya | CIRM H

Post-edited

Research Talks;Algebra;Dynamical Systems and Ordinary Differential Equations;Geometry;Topology

An endomorphism of a finitely generated free group naturally descends to an injective endomorphism on the stable quotient. We establish a geometric incarnation of this fact : an expanding irreducible train track map inducing an endomorphism of the fundamental group determines an expanding irreducible train track representative of the injective endomorphism of the stable quotient. As an application, we prove that the property of having fully irreducible monodromy for a splitting of a hyperbolic free-by-cyclic group G depends only on the component of the BNS invariant $\sum \left ( G \right )$ containing the associated homomorphism to the integers. In particular, it follows that if G is the mapping torus of an atoroidal fully irreducible automorphism of a free group and if the union of $\sum \left ( G \right )$ and $\sum \left ( G \right )$ is connected then for every splitting of $G$ as a (f.g. free)-by-(infinite cyclic) group the monodromy is fully irreducible.
This talk is based on joint work with Spencer Dowdall and Christopher Leininger.
An endomorphism of a finitely generated free group naturally descends to an injective endomorphism on the stable quotient. We establish a geometric incarnation of this fact : an expanding irreducible train track map inducing an endomorphism of the fundamental group determines an expanding irreducible train track representative of the injective endomorphism of the stable quotient. As an application, we prove that the property of having fully ...

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## Automorphisms of hyperbolic groups and growth Horbez, Camille | CIRM H

Post-edited

Research talks;Geometry;Topology

Let $G$ be a torsion-free hyperbolic group, let $S$ be a finite generating set of $G$, and let $f$ be an automorphism of $G$. We want to understand the possible growth types for the word length of $f^n(g)$, where $g$ is an element of $G$. Growth was completely described by Thurston when $G$ is the fundamental group of a hyperbolic surface, and can be understood from Bestvina-Handel's work on train-tracks when $G$ is a free group. We address the general case of a torsion-free hyperbolic group $G$; we show that every element in $G$ has a well-defined exponential growth rate under iteration of $f$, and that only finitely many exponential growth rates arise as $g$ varies in $G$. In addition, we show the following dichotomy: every element of $G$ grows either exponentially fast or polynomially fast under iteration of $f$.
This is a joint work with Rémi Coulon, Arnaud Hilion and Gilbert Levitt.
Let $G$ be a torsion-free hyperbolic group, let $S$ be a finite generating set of $G$, and let $f$ be an automorphism of $G$. We want to understand the possible growth types for the word length of $f^n(g)$, where $g$ is an element of $G$. Growth was completely described by Thurston when $G$ is the fundamental group of a hyperbolic surface, and can be understood from Bestvina-Handel's work on train-tracks when $G$ is a free group. We address the ...

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## Random subgroups, totally non free actions and factor representations Grigorchuk, Rostislav | CIRM H

Post-edited

Research talks;Algebra;Dynamical Systems and Ordinary Differential Equations;Geometry

I will present results of three studies, performed in collaboration with M.Benli, L.Bowen, A.Dudko, R.Kravchenko and T.Nagnibeda, concerning the invariant and characteristic random subgroups in some groups of geometric origin, including hyperbolic groups, mapping class groups, groups of intermediate growth and branch groups. The role of totally non free actions will be emphasized. This will be used to explain why branch groups have infinitely many factor representations of type $II_1$. I will present results of three studies, performed in collaboration with M.Benli, L.Bowen, A.Dudko, R.Kravchenko and T.Nagnibeda, concerning the invariant and characteristic random subgroups in some groups of geometric origin, including hyperbolic groups, mapping class groups, groups of intermediate growth and branch groups. The role of totally non free actions will be emphasized. This will be used to explain why branch groups have infinitely ...

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## The conjugacy problem for polynomially growing elements of $Out(F_{n})$ Feighn, Mark | CIRM H

Post-edited

Research talks

(joint work with Michael Handel) $Out(F_{n}) := Aut(F_{n})/Inn(F_{n})$ denotes the outer automorphism group of the rank n free group $F_{n}$. An element $f$ of $Out(F_{n})$ is polynomially growing if the word lengths of conjugacy classes in Fn grow at most polynomially under iteration by $f$. The existence in $Out(F_{n}), n > 2$, of elements with non-linear polynomial growth is a feature of $Out(F_{n})$ not shared by mapping class groups of surfaces.
To avoid some finite order behavior, we restrict attention to the subset $UPG(F_{n})$ of $Out(F_{n})$ consisting of polynomially growing elements whose action on $H_{1}(F_{n}, Z)$ is unipotent. In particular, if $f$ is polynomially growing and acts trivially on $H_{1}(F_{n}, Z_{3})$ then $f$ is in $UPG(F_{n})$ and further every polynomially growing element of $Out(F_{n})$ has a power that is in $UPG(F_{n})$. The goal of the talk is to describe an algorithm to decide given $f,g$ in $UPG(F_{n})$ whether or not there is h in $Out(F_{n})$ such that $hf h^{-1} = g$.
The conjugacy problem for linearly growing elements of $UPG(F_{n})$ was solved by Cohen-Lustig. Krstic-Lustig-Vogtmann solved the case of linearly growing elements of $Out(F_{n})$.
A key technique is our use of train track representatives for elements of $Out(F_{n})$, a method pioneered by Bestvina-Handel in the early 1990s that has since been ubiquitous in the study of $Out(F_{n})$.
(joint work with Michael Handel) $Out(F_{n}) := Aut(F_{n})/Inn(F_{n})$ denotes the outer automorphism group of the rank n free group $F_{n}$. An element $f$ of $Out(F_{n})$ is polynomially growing if the word lengths of conjugacy classes in Fn grow at most polynomially under iteration by $f$. The existence in $Out(F_{n}), n > 2$, of elements with non-linear polynomial growth is a feature of $Out(F_{n})$ not shared by mapping class groups of ...

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## Combinatorial and additive number theory:CANT 2011 and 2012New York # may 2011 and may 2012 Nathanson, Melvyn B. | Springer 2014

Congrès

- viii; 312 p.
ISBN 978-1-4939-1600-9

Springer proceedings in mathematics & statistics , 0101

Localisation : Colloque 1er étage (NEW)

théorie combinatoire des nombres # nombre premier de Ramanujan # théorème de Kneser # nombre naturel # inégalité de Plünnecke-Ruzsa # décomposition de Zeckendorf # groupe de Grothendieck # quotient de Lerch # quotient de Fermat-Wilson

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## Group theory, combinatorics, and computing.International conference in honor of Daniela Nikolova-Popova's 60th birthday on group theory, combinatorics and computingBoca Raton # october 3-8, 2012 Morse, Robert Fitzgerald ; Nikolova-Popova, Daniela ; Witherspoon, Sarah | American Mathematical Society 2014

Congrès

- xii; 187 p.
ISBN 978-0-8218-9435-4

Contemporary mathematics , 0611

Localisation : Collection 1er étage

théorie des groupes # analyse combinatoire

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## Topology and geometry in dimension three:triangulations, invariants, and geometric structures.Conference in honor of William Jaco's 70th birthday Stillwater # june 4-6, 2010 Li, Weiping ; Bartolini, Loretta ; Johnson, Jesse ; Luo, Feng ; Myers, Robert ; Rubinstein, J. Hyam | American Mathematical Society 2011

Congrès

- ix; 196 p.
ISBN 978-0-8218-5295-8

Contemporary mathematics , 0560

Localisation : Collection 1er étage

variétés de dimensions trois # variétés topologiques

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## Geometric and cohomological group theory.Proceedings of the fourth London Mathematical Society Durham Symposium Kropholler, Peter H. ; Leary, Ian J. ; Martinez-Pérez, Conchita ; Nucinkis, Brita E. A. | Cambridge University Press 2018

Congrès

- x; 266 p.
ISBN 978-1-316-62322-0

London mathematical society lecture note series , 0444

Localisation : Collection 1er étage

théorie des groupes

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## Dynamics and numbers.A special program: Bonn # June 1- July 31, 2014International conference: Bonn # July 21-25, 2014 Kolyada, Sergiy ; Möller, Martin ; Moree, Pieter ; Ward, Thomas | American Mathematical Society 2016

Congrès

- xi; 315 p.
ISBN 978-1-4704-2020-8

Contemporary mathematics , 0669

Localisation : Collection 1er étage

théorie ergodique # algèbre topologique # approximation diophantienne # nombre transcendant # fraction continue # théorie des groupes # groupe de Lie # fonction d'une variable complexe # interpolation # système dynamique # théorie spectrale # opérateur de Markov # transformation de Fourier

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## Dynamical numbers.Interplay between dynamical systems and number theory.A special programm, may 1-july 31, 2009International conference, Bonn # july 20-24, 2009 Kolyada, Sergiy ; Manin, Yuri ; Möller, Martin ; Moree, Pieter ; Ward, Thomas | American Mathematical Society 2010

Congrès

- xi; 242 p.
ISBN 978-0-8218-4958-3

Contemporary mathematics , 0532

Localisation : Collection 1er étage

théorie des nombres # théorie ergodique # algèbre topologique

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## Geometry and topology down under:a conference in honour of Hyam RubinsteinMelbourne # july 11-22, 2011 Hodgson, Craig D. ; Jaco, William H. ; Scharlemann, Martin G. ; Tillmann, Stephan | American Mathematical Society 2013

Congrès

- xxii; 369 p.
ISBN 978-0-8218-8480-5

Contemporary mathematics , 0597

Localisation : Collection 1er étage

topologie de basse dimension # variétés de dimension 3 # groupe hyperbolique de Gromov

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## Geometry, topology and dynamics of character varieties.Based on lectures given at the summer school held at the National University of Singapore's Institute for Mathematical SciencesSingapore # july and august 2010 Goldman, William M. ; Series, Caroline ; Tan, Ser Peow | World Scientific 2012

Congrès

- xi; 349 p.
ISBN 978-981-4401-35-7

Lecture notes series, institute for mathematical sciences, national university of Singapore , 0023

Localisation : Colloque 1er étage (SING)

géométrie hyperbolique # groupe de Klein # variétés # groupe de Lie semi-simple

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## Hyperbolic geometry and geometric group theoryTokyo # July 30 - August 5, 2014 Fujiwara, Koji ; Kojima, Sadayoshi ; Ohshika, Ken'ichi | Mathematical Society of Japan 2017

Congrès

- 280 p.
ISBN 978-4-86497-042-6

Advanced studies in pure mathematics , 0073

Localisation : Collection 1er étage

géométrie hyperbolique # théorie des groupes géométriques

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## Analysis on graphs and its applications:selected papers based on the Isaac Newton Institute for Mathematical Sciences programme#Jan.8-June29 Exner, Pavel ; Keating, J.P. ; Kuchment, Peter ; Sunada, Toshikazu ; Teplyaev, Alexander | American Mathematical Society 2008

Congrès

- xiii, 705 p.
ISBN 978-0-8218-4471-7

Proceedings of symposia in pure mathematics , 0077

Localisation : Collection 1er étage

théorie des graphes # série Dirichlet # fonction zéta # fractals # EDP # théorie des opérateurs # analyse globale # variété # analyse combinatoire # contrôle des systèmes mécaniques # théorie quantique

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## Geometric methods in group theory :AMS special session on ... held at Northeastern University#Oct. 5-6special session at the first joint meeting of the AMS and the Real Sociedad Matematica Espanola#June 18-21 Burillo, Jose ; Cleary, Sean ; Elder, Murray ; Taback, Jennifer ; Ventura, Enric | American Mathematical Society 2005

Congrès

- 230 p.
ISBN 978-0-8218-3362-9

Contemporary mathematics , 0372

Localisation : Collection 1er étage

théorie des groupes # groupe fini # théorie géométrique des groupes # groupe d'Artin # automate # groupe non-abélien libre # produit libre # arbre # propriété résiduelle # action de groupe

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## Géométries à courbure négative ou nulle, groupes discrets et rigiditésGrenoble # 2004 Bessières, L. ; Parreau, Anne ; Rémy, Bertrand | Société Mathématique de France 2009

Congrès

- xxvi, 466 p.
ISBN 978-2-85629-240-2

Séminaires et Congrès , 0018

Localisation : Collection 1er étage

Application bord # application des périodes # application harmonique # automorphisme extérieur # classe d'Euler bornée # classe de Kähler bornée # cohomologie continue bornée # compactification de Thurston # connexion # corps locaux # courbure # courbure négative ou nulle # cône asymptotique # dimension de Hausdorff # dimension topologique # espace de Teichmüller # espace des modules # espace hyperbolique complexe # espace symétrique # espace symétrique Hermitien # espace à courbure négative # espace CAT(0) # exposant critique # formule de Bochner # groupe aléatoire # groupe arithmétique # groupe de Lie # groupe relativement hyperbolique # groupes d'isométries # groupes de Coxeter # géométrie différentielle globale # géométrie hyerbolique # homéomorphisme quasi-conforme # immeuble affine # immeuble de Bruhat-Tits # immeuble sphérique # jacobienne intermédiaire # monodromie # moyennabilité # mélange # méthodes topologiques globales (à la Gromov) # pincement # point fixe # propriété T # quasi-isométrie # représentations unitaires # rigidité # rigidité infinitésimale # réseau cocompact # réseaux superrigidité # surface de Riemann # surface hyperbolique # surfaces cubiques # théorèmes de rigidité # théorèmes de comparaison # topologie de gromov équivariante # variété hyperbolique # variétés de Hadamard # volume minimal # volume simplical Application bord # application des périodes # application harmonique # automorphisme extérieur # classe d'Euler bornée # classe de Kähler bornée # cohomologie continue bornée # compactification de Thurston # connexion # corps locaux # courbure # courbure négative ou nulle # cône asymptotique # dimension de Hausdorff # dimension topologique # espace de Teichmüller # espace des modules # espace hyperbolique complexe # espace symétrique # espace ...

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## Geometric group theory :Geneva and Barcelona conferences#June 20-28 and June 28-July 2 Arzhantseva, Goulnara N. ; Bartholdi, Laurent ; Burillo, Jose ; Ventura, Enric | Birkhäuser 2007

Congrès

- 253 p.
ISBN 978-3-7643-8411-1

Trends in mathematics

Localisation : Colloque 1er étage (GENE)

théorie des groupes # groupes géométriques # algèbre de groupe localement compact

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