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

We define a concordance invariant, ε(K), associated to the knot Floer complex of K, and give a formula for the Ozsváth–Szabó concordance invariant τ of Kp,q, the (p, q)-cable of a knot K, in terms of p, q, τ(K), and ε(K). We also describe the behavior of ε under cabling, allowing one to compute τ of iterated cables. Various properties and applications of ε are also discussed.