Small Dehn surgery and SU(2)
@inproceedings{Baldwin2021SmallDS, title={Small Dehn surgery and SU(2)}, author={John A. Baldwin and Zhenkun Li and Steven Sivek and Fan Ye}, year={2021} }
We prove that the fundamental group of 3-surgery on a nontrivial knot in S 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…
4 Citations
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