Reducible surgeries and Heegaard Floer homology

Jennifer Hom; Tye Lidman; Nicholas Zufelt

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arXiv · 1307.5317

Reducible surgeries and Heegaard Floer homology

Jennifer Hom·Tye Lidman·Nicholas Zufelt

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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.

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Jennifer Hom, Tye Lidman, Nicholas Zufelt. 2013-10-29. Reducible surgeries and Heegaard Floer homology. https://arxiv.org/abs/1307.5317

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