缅北强奸

Title: Growth of stable subgroups in Morse-local-to-global groups.

础产蝉迟谤补肠迟:听Gersten and Short showed that given a quasiconvex subgroup H of a hyperbolic group G, for any finite generating set S of G, the language of geodesics in Cay(G,S) representing elements of H is a regular language. Having a regular language of geodesics is typically useful for understanding the growth function of the respective group/subgroup. For example, Dahmani, Futer, and Wise make use of the above fact to show that non-elementary hyperbolic groups grow exponentially more quickly than their infinite-index quasi-convex subgroups.

A group is said to be MLTG if local Morse quasi-geodesics are global. The class of MLTG include mapping class groups, CAT(0) groups, Teichmuller spaces, graph products of hyperbolic groups, and a large class of hierarchically hyperbolic groups. Stable subgroups of finitely generated groups generalize quasi-convex subgroups of hyperbolic groups, and if the group G is hyperbolic, then the two notions coincide.

We show that given a stable subgroup H of some MLTG group G, for any finite generating set S of G, the language of geodesics representing elements of H is a regular language. As an application, and in the spirit of Dahmani, Futer, and Wise's result above, we show that torsion-free MLTG groups grow exponentially more quickly than their infinite-index stable subgroups. The talk is based on an ongoing project with Cordes, Russell, and Spriano.