Zobrazeno 1 - 10
of 66
pro vyhledávání: '"Coulon, Remi"'
We construct continuum many infinite, simple, characteristic quotients of non-abelian free groups, answering a 1978 question of James Wiegold. The method is very flexible, allowing to impose certain properties on the quotients, to generalize the cons
Externí odkaz:
http://arxiv.org/abs/2312.11684
Autor:
Coulon, Rémi, Dorfsman-Hopkins, Gabriel, Harriss, Edmund, Skrodzki, Martin, Stange, Katherine E., Whitney, Glen
Mathematical understanding is built in many ways. Among these, illustration has been a companion and tool for research for as long as research has taken place. We use the term illustration to encompass any way one might bring a mathematical idea into
Externí odkaz:
http://arxiv.org/abs/2307.04636
Autor:
Coulon, Rémi
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 element. We show that the existence of a contracting isometry is a suffici
Externí odkaz:
http://arxiv.org/abs/2303.01390
Autor:
Coulon, Rémi
Using Patterson-Sullivan measures we investigate growth problems for groups acting on a metric space with a strongly contracting element.
Comment: 61 pages, 2 figures. Slightly different definition of contracting tails. Corrected a mistake in Co
Comment: 61 pages, 2 figures. Slightly different definition of contracting tails. Corrected a mistake in Co
Externí odkaz:
http://arxiv.org/abs/2206.07361
Autor:
Coulon, Rémi, Sela, Zlil
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 instance the Hopf and co-Hopf properties, the isomorphism problem, the
Externí odkaz:
http://arxiv.org/abs/2112.07409
Autor:
Coulon, Rémi, Steenbock, Markus
Publikováno v:
Journal de l'\'Ecole polytechnique - Math\'ematiques 9 (2022), 463-504
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 and Safin for free groups.
Comment: 50 pages, modified definition o
Comment: 50 pages, modified definition o
Externí odkaz:
http://arxiv.org/abs/2102.10885
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 algorithms, independent of the geometry involved. In addition to scenes wit
Externí odkaz:
http://arxiv.org/abs/2010.15801
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 simulation at www.3-dimensional.space/nil.html.
Externí odkaz:
http://arxiv.org/abs/2002.00513
This article presents virtual reality software designed to explore the Sol geometry. The simulation is available on 3-dimensional.space/sol.html
Comment: 8 pages, 10 figures
Comment: 8 pages, 10 figures
Externí odkaz:
http://arxiv.org/abs/2002.00369
Autor:
Coulon, Rémi
Publikováno v:
Algebr. Geom. Topol. 22 (2022) 1497-1510
In this note we produce examples of outer automorphisms of finitely generated groups which have exotic behaviors in terms of growth of conjugacy classes.
Comment: 13 pages, 1 figure
Comment: 13 pages, 1 figure
Externí odkaz:
http://arxiv.org/abs/1908.11668