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

We apply the theory of equivariant Poincaré duality, developed in previous work of the authors, in the special case of cyclic groups C p C_p of prime order to the Nielsen realisation problem for aspherical manifolds. As an application, we remove, in a special case, a technical condition given by Davis–Lück in their work on that problem. Along the way, we will also give a complete characterisation of C p 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.