Volume 11, issue 1 (2011)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
A note on cabling and $L$–space surgeries

Jennifer Hom

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

We prove that the (p,q)–cable of a knot K S3 admits a positive L–space surgery if and only if K admits a positive L–space surgery and qp 2g(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