Equivariant Poincaré duality for cyclic groups of prime order and the Nielsen realisation problem
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917767580483584 |
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| author | Hilman, Kaif Kirstein, Dominik Kremer, Christian |
| author_facet | Hilman, Kaif Kirstein, Dominik Kremer, Christian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_02220 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Equivariant Poincaré duality for cyclic groups of prime order and the Nielsen realisation problem Hilman, Kaif Kirstein, Dominik Kremer, Christian Algebraic Topology Geometric Topology 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. |
| title | Equivariant Poincaré duality for cyclic groups of prime order and the Nielsen realisation problem |
| topic | Algebraic Topology Geometric Topology |
| url | https://arxiv.org/abs/2409.02220 |