Cable links and L-space surgeries

Abstract

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 $n/m\ge 2g(K)-1$. 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.

arXiv comment27 pages, 6 figures, 4 tables; v2: Resolved m=1 case in Theorem 1; minor revisions throughout. This is the version to appear in Quantum Topology