A note on cabling and L-space surgeries

We prove that the (p,q)-cable of a knot K in S^3 admits a positive L-space surgery if and only if K admits a positive L-space surgery and q/p \geq 2g(K)-1, where g(K) is the Seifert genus of K. The "if" direction is due to Hedden.Comment: 3 page

Bordered Heegaard Floer homology and the tau-invariant of cable knots

We define a concordance invariant, epsilon(K), associated to the knot Floer complex of K, and give a formula for the Ozsv\'ath-Szab\'o concordance invariant tau of K_{p,q}, the (p,q)-cable of a knot K, in terms of p, q, tau(K), and epsilon(K). We also describe the behavior of epsilon under cabling, allowing one to compute tau of iterated cables. Various properties and applications of epsilon are also discussed.Comment: 40 pages, 13 figures. v2: minor revisions throughout, 2 additional figures. This is the version to appear in the Journal of Topolog

The knot Floer complex and the smooth concordance group

We define a new smooth concordance homomorphism based on the knot Floer complex and an associated concordance invariant, epsilon. As an application, we show that an infinite family of topologically slice knots are independent in the smooth concordance group.Comment: 25 pages, 5 figure

Cable links and L-space surgeries

An L-space link is a link in $S^3$ on which all sufficiently large integral surgeries are L-spaces. We prove that for m, n relatively prime, the r-component cable link $K_{rm,rn}$ is an L-space link if and only if K is an L-space knot and $n/m \geq 2g(K)-1$. We also compute HFL-minus and HFL-hat of an L-space cable link in terms of its Alexander polynomial. As an application, we confirm a conjecture of Licata regarding the structure of HFL-hat for (n,n) torus links.Comment: 27 pages, 6 figures, 4 tables; v2: Resolved m=1 case in Theorem 1; minor revisions throughout. This is the version to appear in Quantum Topolog