Small Dehn surgery and SU(2)

John A. Baldwin; Zhenkun Li; Steven Sivek; Fan Ye

doi:10.2140/gt.2024.28.1891

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arXiv · 2110.02874

Small Dehn surgery and SU(2)

John A. Baldwin·Zhenkun Li·Steven Sivek·Fan Ye

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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).

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BibTeX RIS

John A. Baldwin, Zhenkun Li, Steven Sivek, Fan Ye. 2021-10-06. Small Dehn surgery and SU(2). https://doi.org/10.2140/gt.2024.28.1891

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