Small Dehn surgery and SU(2)
Abstract
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).
- Publication:
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arXiv e-prints
- Pub Date:
- October 2021
- DOI:
- 10.48550/arXiv.2110.02874
- arXiv:
- arXiv:2110.02874
- Bibcode:
- 2021arXiv211002874B
- Keywords:
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- Mathematics - Geometric Topology
- E-Print:
- 28 pages