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arXiv · 2409.02220

Equivariant Poincar\'e duality for cyclic groups of prime order and the Nielsen realisation problem

Kaif Hilman·Dominik Kirstein·Christian Kremer
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Abstract

In this companion article to [HKK24], we apply the theory of equivariant Poincar\'e 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--L\"uck [DL24] in their work on the Nielsen realisation problem for aspherical manifolds. Along the way, we will also give a complete characterisation of $C_p$--Poincar\'e spaces as well as introduce a genuine equivariant refinement of the classical notion of virtual Poincar\'e duality groups which might be of independent interest.

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Kaif Hilman, Dominik Kirstein, Christian Kremer. 2024-09-03. Equivariant Poincar\'e duality for cyclic groups of prime order and the Nielsen realisation problem. https://arxiv.org/abs/2409.02220

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