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

Abstract

We define a concordance invariant, epsilon(K), associated to the knot Floer complex of K, and give a formula for the Ozsváth-Szabó 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.

40 pages, 13 figures. v2: minor revisions throughout, 2 additional figures. This is the version to appear in the Journal of Topology

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