English

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