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Extending group actions on metric spaces

Presented by: 
Denis Osin Vanderbilt University
Date: 
Thursday 22nd June 2017 - 16:00 to 17:00
Venue: 
INI Seminar Room 1
Abstract: 
I will discuss the following natural extension problem for group actions: Given a group G, a subgroup H of G, and an action of H on a metric space, when is it possible to extend it to an action of the whole group on a (possibly different) metric space? When does such an extension preserve interesting properties of the original action of H? We begin by formalizing this problem and present a construction of an induced action which behaves well when H is hyperbolically embedded in G. Moreover, we show that induced actions can be used to characterize hyperbolically embedded subgroups. 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons