Groups acting on trees and the Eilenberg-Ganea problem for families

Abstract

We construct new examples of groups with cohomological dimension 2 and geometric dimension 3 with respect to the families of finite subgroups, virtually abelian groups of bounded rank, and the family of virtually poly-cyclic subgroups. Our main ingredients are the examples constructed by Brady-Leary-Nucinckis and Fluch-Leary, and Bass-Serre theory.

Version accepted for publication in Proceedings of the AMS. Minor corrections

References in corpus (2)

• Virtually cyclic dimension for 3-manifold groups
• Commensurators of abelian subgroups in CAT(0) groups