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Title:
Research Talk: Every Countable Group is an Outer Automorphism Group of an Acylindrically Hyperbolic Group with Kazhdan's Property (T)
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Abstract:
The combination of Kazhdan’s property (T) and negative curvature typically limits the amount of outer automorphisms. Indeed, it is a result of Paulin that every property (T) hyperbolic group has a finite outer automorphism group. Belegradek and Szczepan ́ski extends Paulin’s result to property (T) relatively hyperbolic groups. We prove that for every countable group Q there is an acylindrically hyperbolic group G such that Out(G) = Q. Therefore the combination of property (T) and acylindrical hyperbolicity is much more flexible in terms of outer automorphisms.
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