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Extending group actions on metric spaces

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NPCW05 - Group actions and cohomology in non-positive curvature

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. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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