Non-Euclidean Virtual Reality IV: Sol
This article presents virtual reality software designed to explore the Sol geometry. The simulation is available on …
Non-Euclidean Virtual Reality III: Nil
We describe a method of rendering real-time scenes in Nil geometry, and use this to give an expository account of some interesting …
Small cancellation theory over Burnside groups
We develop a version of small cancellation theory in the variety of Burnside groups. More precisely, we show that there exists a …
Examples of groups whose automorphisms have exotic growth
In this note we produce examples of outer automorphisms of finitely generated groups which have exotic behaviors in terms of growth of …
Automorphisms and endomorphisms of lacunary hyperbolic groups
In this article we study automorphisms and endomorphisms of lacunary hyperbolic groups. We prove that every lacunary hyperbolic group …
A non-residually finite group acting uniformly properly on a hyperbolic space
In this article we produce an example of a non-residually finite group which admits a uniformly proper action on a Gromov hyperbolic …
Infinite periodic groups of even exponents
We give a new proof that free Burnside groups of sufficiently large even exponents are infinite. The method can also be used to study …
Twisted Patterson-Sullivan measures and applications to amenability and coverings
Let $Γ'<Γ$ be two discrete groups acting properly by isometries on a Gromov-hyperbolic space $X$. We prove that their critical …
Growth gap in hyperbolic groups and amenability
We prove a general version of the amenability conjecture in the unified setting of a Gromov hyperbolic group $G$ acting properly …
Farrell-Jones via Dehn fillings
Following the approach of Dahmani, Guirardel and Osin, we extend the group theoretical Dehn filling theorem to show that the …
Detecting trivial elements of periodic quotient of hyperbolic groups
In this article we give a sufficient and necessary condition to determine whether or not an element of the free group induces a …
Growth and order of automorphisms of free groups and free Burnside groups
We prove that an outer automorphism of the free group is exponentially growing if and only if it induces an outer automorphism of …
Théorie de la petite simplification: une approche géométrique [d'après F. Dahmani, V. Guirardel, D. Osin et S. Cantat, S. Lamy]
Séminaire Bourbaki. Exposé No. 1089
Partial periodic quotients of groups acting on a hyperbolic space
In this article, we construct partial periodic quotients of groups which have a non-elementary acylindrical action on a hyperbolic …
A Cartan-Hadamard type result for relatively hyperbolic groups
In this article, we prove that if a finitely presented group has an asymptotic cone which is tree-graded with respect to a precise set …
On the geometry of Burnside quotients of torsion free hyperbolic groups
In these notes we detail the geometrical approach of small cancellation theory used by T. Delzant and M. Gromov to provide a new proof …
Outer automorphisms of free Burnside groups
In this paper, we study some properties of the outer automorphism group of free Burnside groups of large odd exponent. In particular, …
Growth of periodic quotients of hyperbolic groups
Let $G$ be a non-elementary torsion-free hyperbolic group. We prove that the exponential growth rate of the periodic quotient $G/G^n$ …
Asphericity and small cancellation theory for rotation families of groups
Using small cancellation for rotating families of groups, we construct new examples of aspherical polyhedra.