Equivariant Poincaré duality for cyclic groups of prime order and the Nielsen realisation problem

Abstract

In this companion article to [HKK24], we apply the theory of equivariant Poincaré duality developed there in the special case of cyclic groups $C_p$ of prime order to remove, in a special case, a technical condition given by Davis--Lück [DL24] in their work on the Nielsen realisation problem for aspherical manifolds. Along the way, we will also give a complete characterisation of $C_p$--Poincaré spaces as well as introduce a genuine equivariant refinement of the classical notion of virtual Poincaré duality groups which might be of independent interest.

30 pages. Comments welcome!