Rice University

Events at Rice

Seminar

Mathematics

Speaker: Carolyn Abbott
UWM

Topology Seminar: Universal acylindrical actions

Monday, March 6, 2017
4:00 PM  to 5:00 PM

427  Herman Brown Hall
Rice University
6100 Main St
Houston, Texas, USA

The class of acylindrically hyperbolic groups, which are groups that admit a certain type of non-elementary action on a hyperbolic space, contains many interesting groups such as non-exceptional mapping class groups and Out(F_n) for n>1. In such a group, a generalized loxodromic element is one that is loxodromic for some acylindrical action of the group on a hyperbolic space. Given a finitely generated group, one can look for an acylindrical action on a hyperbolic space in which all generalized loxodromic elements act loxodromically; such an action is called a universal acylindrical action. I will discuss recent results in the search for universal acylindrical actions, describing a class of groups for which it is always possible to construct such an action as well as an example of a group for which no such action exists.

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