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

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

2012-02-07

arxiv.org/abs/1202.1463v1

Mathematics

Geometric Topology

37 pages, 11 figures

Scientific paper

We define a concordance invariant, epsilon(K), associated to the knot Floer complex of K, and give a formula for the Ozsv\'ath-Szab\'o 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.

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