Every finite complex has the homology of some CAT(0) cubical duality group

Abstract

We prove that every finite connected simplicial complex has the homology of the classifying space for some $\mathrm{CAT}(0)$ cubical duality group. More specifically, for any finite simplicial complex $X$, we construct a locally $\mathrm{CAT}(0)$ cubical complex $T_X$ and an acyclic map $t_X:T_X\to X$ such that ${\pi }_1(T_X)$ is a duality group.

11 pages, 3 figures

References in corpus (1)

• Every finite complex is the classifying space for proper bundles of a virtual Poincaré duality group

Cited by in corpus (2)

• On the simplicial volume and the Euler characteristic of (aspherical) manifolds
• Every finite complex is the classifying space for proper bundles of a virtual Poincaré duality group