Finiteness properties

A combination of Bestvina–Brady Morse theory and an acyclic reflection group trick produces a torsion-free finitely presented -Poincaré duality group which is not the fundamental group of an aspherical closed ANR -homology manifold.

The acyclic construction suggests asking which -Poincaré duality groups act freely on -acyclic spaces (i.e., which groups are ). For example, the orbifold fundamental group of a good orbifold satisfies -Poincaré duality, and we show is if the Euler characteristics of certain fixed sets vanish.