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

2024/09/03 by Kaif Hilman, Hilman, Kaif, Dominik Kirstein +3 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Topology (math.AT) #FOS: Mathematics #Finite Group Theory Research #Geometric Topology (math.GT)

paper · pdf · doi:10.48550/arxiv.2409.02220

openalex publication_date 2024/09/03 · openalex created_date 2024/10/11 · openalex updated_date 2026/07/28

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.

Cited by

• Semifree Isovariant Poincaré Spaces and the Gap Condition
• Borel actions in nonpositively curved geometry and the Nielsen realisation problem

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