Mathematical Research Letters
Volume 22 (2015)
Reducible surgeries and Heegaard Floer homology
Pages: 763 – 788
In this paper, we use Heegaard Floer homology to study reducible surgeries. In particular, suppose $K$ is a non-cable knot in $S^3$ with a positive $L$-space surgery. If $p$-surgery on $K$ is reducible, we show that $p = 2g(K)-1$. This implies that any knot with an $L$-space surgery has at most one reducible surgery, a fact that we show additionally for any knot of genus at most two.