Cables of thin knots and bordered Heegaard Floer homology

Abstract

We use bordered Floer homology to give a formula for \widehat{\rm HFK} (K_{p, pn+1}) of any (p, pn+1) -cable of a thin knot K in terms of \Delta_K(t) , \tau(K) , p , and n . We also give a formula for the Ozsváth–Szabó concordance invariant \tau(K_{p, q}) in terms of \tau(K) , p , and q , for all relatively prime p and q .