A Combinatorial Description of the Knot Concordance Invariant Epsilon

Abstract

In this paper, we give a combinatorial description of the concordance invariant $\epsilon$ defined by Hom in \cite{hom2011knot}, prove some properties of this invariant using grid homology techniques. We also compute $\epsilon$ of $(p,q)$ torus knots and prove that $\epsilon ({\mathbb{G}}_{+})=1$ if ${\mathbb{G}}_{+}$ is a grid diagram for a positive braid. Furthermore, we show how $\epsilon$ behaves under $(p,q)$-cabling of negative torus knots.

Some additional figures, further details added to the definitions, accepted to Journal of Knot Theory and Its Ramifications

References in corpus (4)

• Concordance homomorphisms from knot Floer homology
• The knot Floer complex and the smooth concordance group
• Grid Diagrams for Lens Spaces and Combinatorial Knot Floer Homology
• Bordered Heegaard Floer homology and the tau-invariant of cable knots