Semifree Isovariant Poincaré Spaces and the Gap Condition
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918173087891456 |
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| author | Kirstein, Dominik Kremer, Christian |
| author_facet | Kirstein, Dominik Kremer, Christian |
| contents | We introduce the notion of a semifree isovariant $G$-Poincaré space, a homotopical notion interpolating between semifree closed smooth $G$-manifolds and the equivariant Poincaré spaces of [HKK24b]. It carries the additional structure of an equivariant Poincaré embedding of the fixed points of a semifree $G$-Poincaré space. Under suitable gap conditions on the codimension, we show that the space of isovariant structures on a semifree $G$-Poincaré space for a periodic finite group $G$ is highly connected, giving a useful construction tool for manifold structures on equivariant Poincaré spaces. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_23318 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Semifree Isovariant Poincaré Spaces and the Gap Condition Kirstein, Dominik Kremer, Christian Algebraic Topology Geometric Topology 55P91, 57P10, 57R40, 57S17 We introduce the notion of a semifree isovariant $G$-Poincaré space, a homotopical notion interpolating between semifree closed smooth $G$-manifolds and the equivariant Poincaré spaces of [HKK24b]. It carries the additional structure of an equivariant Poincaré embedding of the fixed points of a semifree $G$-Poincaré space. Under suitable gap conditions on the codimension, we show that the space of isovariant structures on a semifree $G$-Poincaré space for a periodic finite group $G$ is highly connected, giving a useful construction tool for manifold structures on equivariant Poincaré spaces. |
| title | Semifree Isovariant Poincaré Spaces and the Gap Condition |
| topic | Algebraic Topology Geometric Topology 55P91, 57P10, 57R40, 57S17 |
| url | https://arxiv.org/abs/2510.23318 |