A note on cabling and L–space surgeries

Hom, Jennifer

doi:10.2140/agt.2011.11.219

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A note on cabling and $L$–space surgeries

Jennifer Hom

Algebraic & Geometric Topology 11 (2011) 219–223

DOI: 10.2140/agt.2011.11.219

Abstract

We prove that the $(p, q)$ –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 $q ∕ p \geq 2 g (K) - 1$ , where $g (K)$ 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

References

Publication

Received: 13 April 2010

Revised: 16 September 2010

Accepted: 18 October 2010

Published: 7 January 2011

Authors

Jennifer Hom
Department of Mathematics University of Pennsylvania 209 S 33rd St Philadelphia PA 19104 USA
http://www.math.upenn.edu/~jenhom

Volume 11, issue 1 (2011)