Volume 11, issue 1 (2011)

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A note on cabling and $L$–space surgeries

Jennifer Hom

Algebraic & Geometric Topology 11 (2011) 219–223
Abstract

We prove that the $\left(p,q\right)$–cable of a knot $K\subset {S}^{3}$ admits a positive $L$–space surgery if and only if $K$ admits a positive $L$–space surgery and $q∕p\ge 2g\left(K\right)-1$, where $g\left(K\right)$ is the Seifert genus of $K$. The “if” direction is due to Hedden [Int. Math. Res. Not. 2009 (2009) 2248–2274].

Keywords
$L$–space, cabling, knot Floer homology, Heegaard Floer homology
Mathematical Subject Classification 2000
Primary: 57M27, 57R58