Extending Properties to Relatively Hyperbolic Groups

Abstract

Consider a finitely generated group $G$ that is relatively hyperbolic with respect to a family of subgroups $H_1,...,H_n$. We present an axiomatic approach to the problem of extending metric properties from the subgroups $H_i$ to the full group $G$. We use this to show that both (weak) finite decomposition complexity and straight finite decomposition complexity are extendable properties. We also discuss the equivalence of two notions of straight finite decomposition complexity.

11 pages

References in corpus (1)

• On the K-theory of groups with Finite Decomposition Complexity

Cited by in corpus (1)

• Coarse amenability and discreteness