Finite automorphisms of negatively curved Poincaré duality groups

Abstract

In this paper, we show that if G is a finite p-group (p prime) acting by automorphisms on a δ-hyperbolic Poincaré Duality group over $\mathbb{Z}$, then the fixed subgroup is a Poincaré Duality group over $\mathbb{Z}_p$. We also provide a family of examples to show that the fixed subgroup might not be a Poincaré Duality group over $\mathbb{Z}$. In fact, the fixed subgroups in our examples even fail to be duality groups over $\mathbb{Z}$.