21.70 (2026)

A group $G$ is called an orientable Poincaré duality group of dimension $n$ over a ring $R$ if it is of type FP over $R$ and $H^i(G; RG) = 0$ for $i \neq n$, while $H^n(G; RG) = R$ as an $RG$-module, where the action on $R$ is trivial. (Note that $G$ is not required to be finitely presented.)

If $G$ is an orientable Poincaré duality group of dimension $n$ over all fields, is it an orientable Poincaré duality group over the integers?