Bicollapsibility and groups with torsion

Abstract

We introduce the notion of a bicollapsible 2-complex. This allows us to generalize the hyperbolicity of one-relator groups with torsion to a broader class of groups with presentations whose relators are proper powers. We also prove that many such groups act properly and cocompactly on a CAT(0) cube complex.

18 pages, 6 figures, comments welcome!