"Geometry and Analysis on Groups" Research Seminar

Time: 2015.12.15, 15:00–17:00
Location: Seminarraum 8, Oskar-Morgenstern-Platz 1, 2.Stock
Title: "Acylindrical hyperbolicity of diagram groups from cubical geometry."
Speaker: Anthony Genevois (Aix-Marseille Université)
Abstract: The first part of the talk will be essentially dedicated to the introduction of the diagram groups and the CAT(0) cube complexes on which they act. Afterwards, the problem we will be interested in is to use this action in order to study some negatively-curved properties of diagram groups, in particular their acylindrical hyperbolicity. Thanks to a general construction due to Bestvina, Bromberg and Fujiwara, a sufficient condition to deduce the acylindrical hyperbolicity of a diagram group is to find contracting isometries in the action on its associated cube complex. The goal of the second part of the talk will be to introduce a characterization of contracting isometries of a CAT(0) cube complex, and then to show how it may be applied to diagram groups, giving a simple method to determine precisely when an element of the group induces or not a contracting isometry of its cube complex.