Homology manifolds and homogeneous compacta
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909607565197312 |
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| author | Valov, Vesko |
| author_facet | Valov, Vesko |
| contents | A non-trivial separable metric space $X$ is called an almost homology $n$-manifold if the homology groups $H_k(X,X\backslash\{x\},\mathbb Z)$ are trivial for all $x\in X$ and all $k=0,1,..,n-1$. We provide a necessary and sufficient condition locally compact homogeneous $ANR$-spaces or strongly locally homogeneous $ANR$-spaces to be almost homology $n$-manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_07196 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Homology manifolds and homogeneous compacta Valov, Vesko General Topology Geometric Topology Primary 54C55, Secondary 55M15 A non-trivial separable metric space $X$ is called an almost homology $n$-manifold if the homology groups $H_k(X,X\backslash\{x\},\mathbb Z)$ are trivial for all $x\in X$ and all $k=0,1,..,n-1$. We provide a necessary and sufficient condition locally compact homogeneous $ANR$-spaces or strongly locally homogeneous $ANR$-spaces to be almost homology $n$-manifolds. |
| title | Homology manifolds and homogeneous compacta |
| topic | General Topology Geometric Topology Primary 54C55, Secondary 55M15 |
| url | https://arxiv.org/abs/2505.07196 |