Four-ball genus bounds and a refinement of the Ozsvath-Szabo tau-invariant

TL;DR

This paper introduces a new concordance invariant derived from the knot Floer complex, which can provide tighter bounds on the 4-ball genus of knots than the existing Ozsvath-Szabo tau-invariant.

Contribution

The authors construct a novel concordance invariant from the knot Floer complex that improves bounds on the 4-ball genus beyond the tau-invariant.

Findings

Invariant can give arbitrarily better bounds than tau-invariant

Constructed explicit examples demonstrating the improvement

Enhances understanding of knot concordance and 4-ball genus bounds

Abstract

Based on work of Rasmussen, we construct a concordance invariant associated to the knot Floer complex, and exhibit examples in which this invariant gives arbitrarily better bounds on the 4-ball genus than the Ozsvath-Szabo tau invariant.