A combinatorial description of the knot concordance invariant epsilon

Abstract

In this paper, we give a combinatorial description of the concordance invariant [Formula: see text] defined by Hom, prove some properties of this invariant using grid homology techniques. We compute the value of [Formula: see text] for [Formula: see text] torus knots and prove that [Formula: see text] if [Formula: see text] is a grid diagram for a positive braid. Furthermore, we show how [Formula: see text] behaves under [Formula: see text]-cabling of negative torus knots.