Reducible surgeries and Heegaard Floer homology
Geometric Topology
2013-10-30 v2
Abstract
In this paper, we use Heegaard Floer homology to study reducible surgeries. In particular, suppose K is a non-cable knot in the three-sphere with an L-space surgery. If p-surgery on K is reducible, we show that p equals 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.
Keywords
Cite
@article{arxiv.1307.5317,
title = {Reducible surgeries and Heegaard Floer homology},
author = {Jennifer Hom and Tye Lidman and Nicholas Zufelt},
journal= {arXiv preprint arXiv:1307.5317},
year = {2013}
}
Comments
15 pages, 2 figures; added an additional author and a new section (3.2) which improves Theorem 1.3