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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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Documents 20F34 | enregistrements trouvés : 23

Automorphisms of hyperbolic groups and growth Horbez, Camille | H Nouveau

Séminaire de géométrie algébrique du Bois Marie 1962-64 SGA 3groupes de type multiplicatif, et structure des schémas en groupes généraux II Artin, Michael ; Bertin, J. E. ; Demazure, M. ; Gabriel, P. ; Grothendieck, A. | 1970 Nouveau

Séminaire N. Bourbaki. Vol. 1997-98exposés 840 à 844 Mars 1988 Bourbaki, N. | 1998 Nouveau

Recent developpements in the inverse Galois problem Abhyankar, Shreeram Shankar ; Feit, Walter ; Fried, Michael D. ; Ihara, Yasutaka ; Voelklein, Helmut | 1995 Nouveau

Arithmetic fundamental groups and noncommutative algebra :1999 von Neumann conference on ... held at the Mathematical Sciences Research Institute#Aug. 16-27 Fried, Michael D. ; Ihara, Yasutaka | 2002 Nouveau

Arrangements, local systems and singularitiesCIMPA summer schoolIstanbul # june 11-22, 2007 El Zein, Fouad ; Suciu, Alexander I. ; Tosun, Meral ; Uludag, A. Muhammed ; Yuzvinsky, Sergey | 2010 Nouveau

Sovremennye problemy matematiki. fundamental'nye napravleniya. Tom 46 [Les problèmes actuels des mathématiques. Les directions fondamentales] :algebra. 7[algèbre. 7] Gamkrelidze, R. | 1985 Nouveau

Equations différentielles à points singuliers réguliers Deligne, Pierre | 1970 Nouveau

Espaces de modules des courbes, groupes modulaires et théorie des champs Buff, Xavier ; Fehrenbach, Jérôme ; Lochak, Pierre ; Schneps, Leila ; Vogel, Pierre | 1999 Nouveau

Les groupes fondamentaux et les produits fondamentaux de groupes Piccard, Sophie | 1981 Nouveau

Generators and relations for discrete groups Coxeter, H. S. M. ; Moser, W. O. J. | 1965 Nouveau

Subgroups of Teichmüller modular groups Ivanov, Nikolai V. | 1992 Nouveau

Topology :an introduction with application to topological groups McCarty, George | 1967 Nouveau

Homotopy equivalences of 3-manifolds and deformation theory of kleinian groups Canary, Richard D. ; McCullough, Darryl | 2004 Nouveau

Moduli spaces of curves, mapping class groups and field theory Buff, Xavier ; Fehrenbach, Jérôme ; Lochak, Pierre ; Schneps, Leila | 2002 Nouveau

Fundamental groups and covering spaces Lima, Elon Lages ; Gomes, Jonas | 2003 Nouveau

Knots Burde, Gerhard ; Zieschang, Heiner | 2002 Nouveau

Problems on mapping class groups and related topics Farb, Benson | 2006 Nouveau

Ordering braids Dehornoy, Patrick ; Dynnikov, Ivan ; Rolfsen, Dale ; Wiest, Bert | 2008 Nouveau

Geometric group theory Drutu, Cornelia ; Kapovich, Michael ; Nica, Bogdan | 2018 Nouveau

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Séminaire de géométrie algébrique du Bois Marie 1962-64 SGA 3
groupes de type multiplicatif, et structure des schémas en groupes généraux II Artin, Michael ; Bertin, J. E. ; Demazure, M. ; Gabriel, P. ; Grothendieck, A. | 1970 Nouveau

Séminaire N. Bourbaki. Vol. 1997-98
exposés 840 à 844 Mars 1988 Bourbaki, N. | 1998 Nouveau

Arithmetic fundamental groups and noncommutative algebra :
1999 von Neumann conference on ... held at the Mathematical Sciences Research Institute#Aug. 16-27 Fried, Michael D. ; Ihara, Yasutaka | 2002 Nouveau

Arrangements, local systems and singularities
CIMPA summer school
Istanbul # june 11-22, 2007 El Zein, Fouad ; Suciu, Alexander I. ; Tosun, Meral ; Uludag, A. Muhammed ; Yuzvinsky, Sergey | 2010 Nouveau

Sovremennye problemy matematiki. fundamental'nye napravleniya. Tom 46 [Les problèmes actuels des mathématiques. Les directions fondamentales] :
algebra. 7[algèbre. 7] Gamkrelidze, R. | 1985 Nouveau

Topology :
an introduction with application to topological groups McCarty, George | 1967 Nouveau