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# Documents  Short, Hamish | enregistrements trouvés : 3

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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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## Exceptional 3-manifolds​ Friedl, Stefan | CIRM H

Multi angle

Research talks;Geometry;Topology

We say a manifold $M$ is exceptional if for any $n$ all degree $n$ covers of $M$ are homeomorphic. For example closed surfaces and all tori are exceptional. We classify exceptional 3-manifolds.
This is based on joint work with Junghwan Park, Bram Petri and Aru Ray.

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## The geometry of the word problem for finitely generated groups Brady, Noel ; Riley, Tim ; Short, Hamish | Birkhäuser Verlag 2007

Ouvrage

- 206 p.
ISBN 978-3-7643-7949-0

Advanced courses in mathematics CRM Barcelona

théorie des groupes géométriques # problème de mot # groupe hyperbolique # propriétés asymptotiques des groupes # méthode homologique # méthode topologique # diagramme de Kampon # graphe de Cayley # fonction isopérimétrique # fonction de Dehn # groupe à courbure négative # CAT(O) groupe # groupe nilpotent

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