Signature and concordance of positive knots

TL;DR

This paper establishes a linear relationship between the signature and genus of positive knots and demonstrates that each knot concordance class contains only finitely many positive knots.

Contribution

It introduces a linear estimate of the signature for positive knots and applies it to show finiteness within knot concordance classes.

Findings

Linear estimate of signature in terms of genus

Finiteness of positive knots in each concordance class

Advances understanding of positive knot properties

Abstract

We derive a linear estimate of the signature of positive knots, in terms of their genus. As an application, we show that every knot concordance class contains at most finitely many positive knots.