Small Dehn surgery and SU(2)
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866909261816135680 |
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| author | Baldwin, John A. Li, Zhenkun Sivek, Steven Ye, Fan |
| author_facet | Baldwin, John A. Li, Zhenkun Sivek, Steven Ye, Fan |
| contents | We prove that the fundamental group of 3-surgery on a nontrivial knot in the 3-sphere always admits an irreducible SU(2)-representation. This answers a question of Kronheimer and Mrowka dating from their work on the Property P conjecture. An important ingredient in our proof is a relationship between instanton Floer homology and the symplectic Floer homology of genus-2 surface diffeomorphisms, due to Ivan Smith. We use similar arguments at the end to extend our main result to infinitely many surgery slopes in the interval [3,5). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_02874 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Small Dehn surgery and SU(2) Baldwin, John A. Li, Zhenkun Sivek, Steven Ye, Fan Geometric Topology We prove that the fundamental group of 3-surgery on a nontrivial knot in the 3-sphere always admits an irreducible SU(2)-representation. This answers a question of Kronheimer and Mrowka dating from their work on the Property P conjecture. An important ingredient in our proof is a relationship between instanton Floer homology and the symplectic Floer homology of genus-2 surface diffeomorphisms, due to Ivan Smith. We use similar arguments at the end to extend our main result to infinitely many surgery slopes in the interval [3,5). |
| title | Small Dehn surgery and SU(2) |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2110.02874 |