The Goeritz groups of $(1,1)$-decompositions
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929687325835264 |
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| author | Koda, Yuya Tanaka, Yuki |
| author_facet | Koda, Yuya Tanaka, Yuki |
| contents | A $(g, n)$-decomposition of a link $L$ in a closed orientable $3$-manifold $M$ is a decomposition of $M$ by a closed orientable surface of genus $g$ into two handebodies each intersecting the link $L$ in $n$ trivial arcs. The Goeritz group of that decomposition is then defined to be the group of isotopy classes of orientation-preserving homeomorphisms of the pair $(M, L)$ that preserve the decomposition. We compute the Goeritz groups of all $(1,1)$-decompositions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_15809 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Goeritz groups of $(1,1)$-decompositions Koda, Yuya Tanaka, Yuki Geometric Topology 57K20, 57K10 A $(g, n)$-decomposition of a link $L$ in a closed orientable $3$-manifold $M$ is a decomposition of $M$ by a closed orientable surface of genus $g$ into two handebodies each intersecting the link $L$ in $n$ trivial arcs. The Goeritz group of that decomposition is then defined to be the group of isotopy classes of orientation-preserving homeomorphisms of the pair $(M, L)$ that preserve the decomposition. We compute the Goeritz groups of all $(1,1)$-decompositions. |
| title | The Goeritz groups of $(1,1)$-decompositions |
| topic | Geometric Topology 57K20, 57K10 |
| url | https://arxiv.org/abs/2403.15809 |