Three-Dimensional Small Covers and Links
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915767561224192 |
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| author | Gorchakov, Vladimir |
| author_facet | Gorchakov, Vladimir |
| contents | We study certain orientation-preserving involutions on three-dimensional small covers. We prove that the quotient space of an orientable three-dimensional small cover by such an involution in $\mathbb{Z}_2^3$ is homeomorphic to a connected sum of copies of $S^2 \times S^1$. If this quotient space is a 3-sphere, then the corresponding small cover is a two-fold branched covering of the 3-sphere along a link. We provide a description of this link in terms of the polytope and the characteristic function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_12557 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Three-Dimensional Small Covers and Links Gorchakov, Vladimir Algebraic Topology Combinatorics Geometric Topology 57S12, 57S17, 57S25, 57M60, 52B10 We study certain orientation-preserving involutions on three-dimensional small covers. We prove that the quotient space of an orientable three-dimensional small cover by such an involution in $\mathbb{Z}_2^3$ is homeomorphic to a connected sum of copies of $S^2 \times S^1$. If this quotient space is a 3-sphere, then the corresponding small cover is a two-fold branched covering of the 3-sphere along a link. We provide a description of this link in terms of the polytope and the characteristic function. |
| title | Three-Dimensional Small Covers and Links |
| topic | Algebraic Topology Combinatorics Geometric Topology 57S12, 57S17, 57S25, 57M60, 52B10 |
| url | https://arxiv.org/abs/2408.12557 |