Extendable periodic automorphisms of closed surfaces over the 3-sphere
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866914982331940864 |
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| author | Wang, Chao Wang, Weibiao |
| author_facet | Wang, Chao Wang, Weibiao |
| contents | A periodic automorphism of a surface $Σ$ is said to be extendable over $S^3$ if it extends to a periodic automorphism of the pair $(S^3,Σ)$ for some possible embedding $Σ\to S^3$. We classify and construct all extendable automorphisms of closed surfaces, with orientation-reversing cases included. Moreover, they can all be induced by automorphisms of $S^3$ on Heegaard surfaces. As a by-product, the embeddings of surfaces into lens spaces are discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_06542 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Extendable periodic automorphisms of closed surfaces over the 3-sphere Wang, Chao Wang, Weibiao Geometric Topology 57M60, 57S17, 57S25 A periodic automorphism of a surface $Σ$ is said to be extendable over $S^3$ if it extends to a periodic automorphism of the pair $(S^3,Σ)$ for some possible embedding $Σ\to S^3$. We classify and construct all extendable automorphisms of closed surfaces, with orientation-reversing cases included. Moreover, they can all be induced by automorphisms of $S^3$ on Heegaard surfaces. As a by-product, the embeddings of surfaces into lens spaces are discussed. |
| title | Extendable periodic automorphisms of closed surfaces over the 3-sphere |
| topic | Geometric Topology 57M60, 57S17, 57S25 |
| url | https://arxiv.org/abs/2111.06542 |