48 citations · 144 across the 24 of their papers we have counts for
25 papers
On the growth spectrum of hyperbolic groups
Rémi Coulon, Michail Louvaris, Daniel T. Wise +1
We study the growth spectrum of groups acting on hyperbolic spaces, i.e.\ the set of exponential growth rates achieved by subgroups. For a finitely generated free group or a surfac…
PolExp growth for automorphisms of toral relatively hyperbolic groups
Rémi Coulon, Arnaud Hilion, Camille Horbez +1
Let be a toral relatively hyperbolic group, and let . We prove that, under iteration of , the conjugacy length of every element gr…
Ergodicity of the geodesic flow for groups with a contracting element
Rémi Coulon
In this article we investigate the dynamical properties of the geodesic flow for a proper metric space endowed with a proper action by isometries of a group with a contracting elem…
Patterson-Sullivan theory for groups with a strongly contracting element
Rémi Coulon
Using Patterson-Sullivan measures we investigate growth problems for groups acting on a metric space with a strongly contracting element.
Equations in Burnside groups
Rémi Coulon, Zlil Sela
This article is a first step in the study of equations in periodic groups. As an application, we study the structure of periodic quotients of hyperbolic groups. We investigate for…
Product set growth in Burnside groups
Rémi Coulon, Markus Steenbock
Given a periodic quotient of a torsion-free hyperbolic group, we provide a fine lower estimate of the growth function of any sub-semi-group. This generalizes results of Razborov an…
Ray-marching Thurston geometries
Rémi Coulon, Elisabetta A. Matsumoto, Henry Segerman +1
We describe algorithms that produce accurate real-time interactive in-space views of the eight Thurston geometries using ray-marching. We give a theoretical framework for our algor…
Non-Euclidean Virtual Reality III: Nil
Rémi Coulon, Elisabetta A. Matsumoto, Henry Segerman +1
We describe a method of rendering real-time scenes in Nil geometry, and use this to give an expository account of some interesting geometric phenomena. You can play around with the…
Non-Euclidean Virtual Reality IV: Sol
Rémi Coulon, Elisabetta A. Matsumoto, Henry Segerman +1
This article presents virtual reality software designed to explore the Sol geometry. The simulation is available on 3-dimensional.space/sol.html
Examples of groups whose automorphisms have exotic growth
Rémi Coulon
In this note we produce examples of outer automorphisms of finitely generated groups which have exotic behaviors in terms of growth of conjugacy classes.
Twisted Patterson-Sullivan measures and applications to amenability and coverings
Rémi Coulon, Rhiannon Dougall, Barbara Schapira +1
Let be two discrete groups acting properly by isometries on a Gromov-hyperbolic space . We prove that their critical exponents coincide if and only if is co-amenable…
Infinite periodic groups of even exponents
Rémi Coulon
We give a new proof that free Burnside groups of sufficiently large even exponents are infinite. The method is very flexible and can also be used to study (partially) periodic quot…
A non-residually finite group acting uniformly properly on a hyperbolic space
Rémi Coulon, Denis Osin
In this article we produce an example of a non-residually finite group which admits a uniformly proper action on a Gromov hyperbolic space.
Growth gap in hyperbolic groups and amenability
Rémi Coulon, Françoise Dal'Bo, Andrea Sambusetti
We prove a general version of the amenability conjecture in the unified setting of a Gromov hyperbolic group G acting properly cocompactly either on its Cayley graph, or on a CAT(-…
Small cancellation theory over Burnside groups
Rémi Coulon, Dominik Gruber
We develop a version of small cancellation theory in the variety of Burnside groups. More precisely, we show that there exists a critical exponent such that for every odd int…
Automorphisms and endomorphisms of lacunary hyperbolic groups
Rémi Coulon, Vincent Guirardel
In this article we study automorphisms and endomorphisms of lacunary hyperbolic groups. We prove that every lacunary hyperbolic group is Hopfian, answering a question by Henry Wilt…
Farrell-Jones via Dehn fillings
Yago Antolín, Rémi Coulon, Giovanni Gandini
Following the approach of Dahmani, Guirardel and Osin, we extend the group theoretical Dehn filling theorem to show that the pre-images of infinite order elements have a certain st…
Partial periodic quotient of groups acting on a hyperbolic space
Rémi Coulon
In this article, we construct partial periodic quotients of groups which have a non-elementary acylindrical action on a hyperbolic space. In particular, we provide infinite quotien…
A Cartan-Hadamard type result for relatively hyperbolic groups
Rémi Coulon, Michael Hull, Curtis Kent
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 of pieces then it is relatively hyperbolic. T…
Growth and order of automorphisms of free groups and free Burnside groups
Rémi Coulon, Arnaud Hilion
We prove that an outer automorphism of the free group is exponentially growing if and only if it induces an outer automorphism of infinite order of free Burnside groups with suffic…
Small cancellation theory and Burnside problem
Rémi Coulon
In these notes we detail the geometrical approach of small cancellation theory used by T. Delzant and M. Gromov to provide a new proof of the infiniteness of free Burnside groups a…
Growth of periodic quotients of hyperbolic groups
Rémi Coulon
Let G be a non-elementary torsion-free hyperbolic group. We prove that the exponential growth rate of the periodic quotient G/G^n tends to the one of G as n odd approaches infinity…
A criterion for detecting trivial elements of Burnside groups
Rémi Coulon
In this article we give a sufficient and necessary condition to determine wether or not an element of the free group induces a non-trivial element of the free Burnside group of suf…
Outer automorphisms of free Burnside groups
Rémi Coulon
In this paper, we study some properties of the outer automorphism group of free Burnside groups of large odd exponent. In particular, we prove that it contains free and free abelia…