Distinguishing 2-knots admitting circle actions by fundamental groups
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929439195004928 |
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| author | Fukuda, Mizuki Ishikawa, Masaharu |
| author_facet | Fukuda, Mizuki Ishikawa, Masaharu |
| contents | A 2-sphere embedded in the 4-sphere invariant under a circle action is called a branched twist spin. A branched twist spin is constructed from a 1-knot in the 3-sphere and a pair of coprime integers uniquely. In this paper, we study, for each pair of coprime integers, if two different 1-knots yield the same branched twist spin, and prove that such a pair of 1-knots does not exist in most cases. Fundamental groups of 3-orbifolds of cyclic type are obtained as quotient groups of the fundamental groups of the complements of branched twist spins. We use these groups for distinguishing branched twist spins. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_06276 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Distinguishing 2-knots admitting circle actions by fundamental groups Fukuda, Mizuki Ishikawa, Masaharu Geometric Topology 57Q45 (Primary) 57M05, 57M10, 57M27 (Secondary) A 2-sphere embedded in the 4-sphere invariant under a circle action is called a branched twist spin. A branched twist spin is constructed from a 1-knot in the 3-sphere and a pair of coprime integers uniquely. In this paper, we study, for each pair of coprime integers, if two different 1-knots yield the same branched twist spin, and prove that such a pair of 1-knots does not exist in most cases. Fundamental groups of 3-orbifolds of cyclic type are obtained as quotient groups of the fundamental groups of the complements of branched twist spins. We use these groups for distinguishing branched twist spins. |
| title | Distinguishing 2-knots admitting circle actions by fundamental groups |
| topic | Geometric Topology 57Q45 (Primary) 57M05, 57M10, 57M27 (Secondary) |
| url | https://arxiv.org/abs/2304.06276 |