Constricting elements and the growth of quasi-convex subgroups

Abstract: Let \(G\) be a group acting properly on a metric space \(X\) and consider a path system of \(X\). Assume that \(G\) contains a constricting element with respect to this path system, i.e. a very general condition of non-positive curvature. This talk will be about the relative growth and the coset growth of the quasi-convex subgroups of \(G\) with respect to this path system. Through the triangle inequality, we will see that we can determine that the first kind of growth rates are strictly smaller than the growth rate of \(G\), while the second kind of growth rates coincide with the growth rate of \(G\). Applications include actions of relatively hyperbolic groups, CAT(0) groups with Morse elements and mapping class groups. This generalises work of Antolín, Dahmani-Futer-Wise and Gitik-Rips.

algebraic topologyfunctional analysisgroup theorygeometric topologyoperator algebras

Audience: researchers in the topic

Vienna Geometry and Analysis on Groups Seminar