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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.06350 |
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| _version_ | 1866916387880960000 |
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| author | Harris, Reid |
| author_facet | Harris, Reid |
| contents | The extended mapping class group of a surface $Σ$ is defined to be the group of isotopy classes of (not necessarily orientation-preserving) homeomorphisms of $Σ$. We are able to show that the extended mapping class group of an $n$-punctured sphere is generated by two elements of finite order exactly when $n\not=4$. We use this result to prove that the extended mapping class group of a genus 2 surface is generated by two elements of finite order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_06350 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generating Extended Mapping Class Groups with Two Periodic Elements Harris, Reid Geometric Topology Group Theory The extended mapping class group of a surface $Σ$ is defined to be the group of isotopy classes of (not necessarily orientation-preserving) homeomorphisms of $Σ$. We are able to show that the extended mapping class group of an $n$-punctured sphere is generated by two elements of finite order exactly when $n\not=4$. We use this result to prove that the extended mapping class group of a genus 2 surface is generated by two elements of finite order. |
| title | Generating Extended Mapping Class Groups with Two Periodic Elements |
| topic | Geometric Topology Group Theory |
| url | https://arxiv.org/abs/2409.06350 |