Reducing spheres and weak reducing pairs for Heegaard surfaces in the $3$-sphere
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918150453329920 |
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| author | Cho, Sangbum Koda, Yuya Lee, Jung Hoon |
| author_facet | Cho, Sangbum Koda, Yuya Lee, Jung Hoon |
| contents | Given a Heegaard surface in the $3$-sphere, we show that any non-separating weak reducing pair for the surface admits a reducing sphere that separates the two disks of the pair if and only if the genus of the surface is at most $3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_24388 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reducing spheres and weak reducing pairs for Heegaard surfaces in the $3$-sphere Cho, Sangbum Koda, Yuya Lee, Jung Hoon Geometric Topology 57K30 Given a Heegaard surface in the $3$-sphere, we show that any non-separating weak reducing pair for the surface admits a reducing sphere that separates the two disks of the pair if and only if the genus of the surface is at most $3$. |
| title | Reducing spheres and weak reducing pairs for Heegaard surfaces in the $3$-sphere |
| topic | Geometric Topology 57K30 |
| url | https://arxiv.org/abs/2509.24388 |