A note on reducing spheres for the genus-4 Heegaard surface in the 3-sphere
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910138812596224 |
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| author | Cho, Sangbum Koda, Yuya Lee, Jung Hoon |
| author_facet | Cho, Sangbum Koda, Yuya Lee, Jung Hoon |
| contents | For the genus-$4$ Heegaard surface in the $3$-sphere, we present a sufficient condition for a non-separating weak reducing pair to be separated by a reducing sphere for the surface. As a consequence, we reduce the connectivity problem in the reducing sphere complex for the surface to the problem of showing that any two vertices, whose representative reducing spheres are disjoint from a fixed non-separating compressing disk for the surface, are connected in the complex. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_15722 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A note on reducing spheres for the genus-4 Heegaard surface in the 3-sphere Cho, Sangbum Koda, Yuya Lee, Jung Hoon Geometric Topology 57K30 For the genus-$4$ Heegaard surface in the $3$-sphere, we present a sufficient condition for a non-separating weak reducing pair to be separated by a reducing sphere for the surface. As a consequence, we reduce the connectivity problem in the reducing sphere complex for the surface to the problem of showing that any two vertices, whose representative reducing spheres are disjoint from a fixed non-separating compressing disk for the surface, are connected in the complex. |
| title | A note on reducing spheres for the genus-4 Heegaard surface in the 3-sphere |
| topic | Geometric Topology 57K30 |
| url | https://arxiv.org/abs/2604.15722 |