Mathematical Research Letters

Volume 22 (2015)

Number 3

Reducible surgeries and Heegaard Floer homology

Pages: 763 – 788

DOI: http://dx.doi.org/10.4310/MRL.2015.v22.n3.a8

Authors

Jennifer Hom (Department of Mathematics, Columbia University, New York, N.Y., U.S.A.)

Tye Lidman (Department of Mathematics, The University of Texas, Austin, Tx., U.S.A.)

Nicholas Zufelt (Department of Mathematics, The University of Texas, Austin, Tx., U.S.A.)

Abstract

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.

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