Computable bounds for Rasmussen's concordance invariant

TL;DR

This paper introduces computable bounds for Rasmussen's s-invariant of knots based on diagrams, improving existing bounds on the slice genus under certain conditions.

Contribution

It provides a method to compute bounds for s(K) from knot diagrams and demonstrates their tightness under specific conditions, enhancing slice genus estimates.

Findings

Bounds are easily computable from diagrams.

Bounds are tight for diagrams satisfying certain conditions.

Improves on previous Bennequin-type bounds on slice genus.

Abstract

Given a diagram D of a knot K, we give easily computable bounds for Rasmussen's concordance invariant s(K). The bounds are not independent of the diagram D chosen, but we show that for diagrams satisfying a given condition the bounds are tight. As a corollary we improve on previously known Bennequin-type bounds on the slice genus.