Uniqueness in Haken's Theorem
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2020
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866929470220271616 |
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| author | Freedman, Michael Scharlemann, Martin |
| author_facet | Freedman, Michael Scharlemann, Martin |
| contents | Following Haken and Casson-Gordon, it was shown in [Sc] that given a reducing sphere or boundary-reducing disk E in a Heegaard split manifold M, the Heegaard surface T can be isotoped so that it intersects E in a single circle. Here we show that when this is achieved by two different positionings of T, one can be moved to the other by a sequence of
1) isotopies of T rel E
2) pushing a stabilizing pair of T through E and
3) eyegelass twists of T.
The last move is inspired by one of Powell's proposed generators for the Goeritz group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2004_07385 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Uniqueness in Haken's Theorem Freedman, Michael Scharlemann, Martin Geometric Topology 57K35 Following Haken and Casson-Gordon, it was shown in [Sc] that given a reducing sphere or boundary-reducing disk E in a Heegaard split manifold M, the Heegaard surface T can be isotoped so that it intersects E in a single circle. Here we show that when this is achieved by two different positionings of T, one can be moved to the other by a sequence of 1) isotopies of T rel E 2) pushing a stabilizing pair of T through E and 3) eyegelass twists of T. The last move is inspired by one of Powell's proposed generators for the Goeritz group. |
| title | Uniqueness in Haken's Theorem |
| topic | Geometric Topology 57K35 |
| url | https://arxiv.org/abs/2004.07385 |