Manifold structures on highly connected Poincaré complexes
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908496136503296 |
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| author | Shen, Wen |
| author_facet | Shen, Wen |
| contents | This paper constructs numerous examples of highly connected Poincaré complexes, each homotopy equivalent to a topological manifold yet not homotopy equivalent to any smooth manifold. Furthermore, we determine the homotopy type of any closed $2k$-connected framed $(4k+2)$-manifold with Kervaire invariant one for $k=7,15,31$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23228 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Manifold structures on highly connected Poincaré complexes Shen, Wen Algebraic Topology Geometric Topology This paper constructs numerous examples of highly connected Poincaré complexes, each homotopy equivalent to a topological manifold yet not homotopy equivalent to any smooth manifold. Furthermore, we determine the homotopy type of any closed $2k$-connected framed $(4k+2)$-manifold with Kervaire invariant one for $k=7,15,31$. |
| title | Manifold structures on highly connected Poincaré complexes |
| topic | Algebraic Topology Geometric Topology |
| url | https://arxiv.org/abs/2507.23228 |