Coherence and Negative Sectional Curvature in Complexes of Groups

Abstract

We examine a condition on a simply connected 2-complex X ensuring that groups acting properly on X are coherent. This extends earlier work on 2-complexes with negative sectional curvature which covers the case that G acts freely. Our extension of these results involves a generalization of the notion of sectional curvature, an extension of the combinatorial Gauss-Bonnet theorem to complexes of groups, and surprisingly requires the use of L^2-Betti numbers. We also prove local quasiconvexity of G under the additional assumption that X is CAT(0) space.

Version to appear in Michigan Mathematical Journal

References in corpus (1)

• Local Quasiconvexity of Groups acting on Small Cancellation Complexes

Cited by in corpus (1)

• Lifting Group Actions, Equivariant Towers and Subgroups of Non-positively Curved Groups