Random subgroups, automorphisms, splittings

2019/06/23 by Guirardel, Vincent, Levitt, Gilbert
#FOS: Mathematics #General Topology (math.GN) #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1906.09654

Abstract

We show that, if H is a random subgroup of a finitely generated free group F_k, only inner automorphisms of F_k may leave H invariant. A similar result holds for random subgroups of toral relatively hyperbolic groups, more generally of groups which are hyperbolic relative to slender subgroups. These results follow from non-existence of splittings over slender groups which are relative to a random group element. Random subgroups are defined using random walks or balls in a Cayley tree of F_k.

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