Every finite complex is the classifying space for proper bundles of a virtual Poincaré duality group
arXiv:1209.4846
Abstract
We prove that every finite connected simplicial complex is homotopy equivalent to the quotient of a contractible manifold by proper actions of a virtually torsion-free group. As a corollary, we obtain that every finite connected simplicial complex is homotopy equivalent to the classifying space for proper bundles of some virtual Poincaré duality group.
8 pages