Extending acylindrical actions

Carolyn Abbott (Wisconsin)

Abstract: Given a group G and a subgroup H, it is natural to ask when an action of H on a metric space can be extended to an action of G on a (possibly different) metric space. One might further ask when this extension preserves certain properties of the action of H, such as acylindricity of the action and hyperbolicity of the space. I will discuss when such an extension is possible for a certain class of subgroups of acylindrically hyperbolic groups. I will also give applications of this result to universal acylindrical actions.