A further note on the concordance invariants epsilon and Upsilon

TL;DR

This paper explores the relationship between the epsilon and Upsilon invariants in knot theory, providing new examples of knots with specific invariant properties and demonstrating their independence in the smooth concordance group.

Contribution

It constructs additional knots with vanishing Upsilon but nonzero epsilon invariants, showing their linear independence in the concordance group.

Findings

Identified knots with vanishing Upsilon and nonzero epsilon invariants.

Proved these knots are linearly independent in the smooth concordance group.

Abstract

Hom gives an example of a knot with vanishing Upsilon invariant but nonzero epsilon invariant. We build more such knots that are linearly independent in the smooth concordance group.