Small Dehn surgery and SU(2)

Abstract

Small Dehn surgery and SU.2/ JOHN A BALDWIN ZHENKUN LI STEVEN SIVEK FAN YEWe prove that the fundamental group of 3-surgery on a nontrivial knot in S 3 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 OE3; 5/.