Bi-exactness of relatively hyperbolic groups

2022/07/17 by Oyakawa, Koichi · 2 citations
#FOS: Mathematics #Group Theory (math.GR) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2207.08113

Abstract

We prove that finitely generated relatively hyperbolic groups are bi-exact if and only if all peripheral subgroups are bi-exact. This is a generalization of Ozawa's result which claims that finitely generated relatively hyperbolic groups are bi-exact if all peripheral subgroups are amenable.

Cited by

• Strong solidity classification of Coxeter groups
• Relative solidity results and their applications to computations of some II₁ factor invariants

Related

• Algorithmic Properties of Relatively Hyperbolic Groups
• Boundary Amenability of Relatively Hyperbolic Groups
• Finiteness properties and Relatively Hyperbolic Groups
• Relatively hyperbolic groups: geometry and quasi-isometric invariance
• Fillings, finite generation and direct limits of relatively hyperbolic groups