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 Krm,rn is an L-space link if and only if K is an L-space knot and n/m ≥ 2g(K)-1 . We also compute HFL^– and {HFL} of an L-space cable link in terms of its Alexander polynomial. As an application, we confirm a conjecture of Licata [7] regarding the structure of {HFL} for (n,n) torus links.