Transactions of the American Mathematical Society Series B· 2026Q1
Equivariant Poincaré duality for cyclic groups of prime order and the Nielsen realisation problem
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- Q1SCImago
- 2026year
Short summary
New equivariant Poincaré duality theory for cyclic groups of prime order (Cp) simplifies the Nielsen realisation problem for aspherical manifolds, removing a technical condition by Davis–Lück.
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Key points
- Equivariant Poincaré duality theory is applied to cyclic groups of prime order (Cp).
- A technical condition by Davis–Lück in the Nielsen realisation problem is removed for a special case.
- Cp-Poincaré spaces are completely characterized.
- A new equivariant refinement of virtual Poincaré duality groups is introduced.
AI-generated from the title and abstract; the full text is not read.
Abstract
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.
The authors' abstract, as published at the source. Transactions of the American Mathematical Society Series B, 2026 · DOI ↗
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Field: Geometry and Topology
Geometry and TopologyMathematics