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 ⊂ S³ admits a positive L–space surgery if and only if K admits a positive L–space surgery and q ∕ p ≥ 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

Primary: 57M27, 57R58

References

Publication

Received: 13 April 2010
Revised: 16 September 2010
Accepted: 18 October 2010
Published: 7 January 2011

Authors