On the signature of a positive braid

TL;DR

This paper establishes a new lower bound for the signature of positive braid links, relating it to their first Betti number, and improves upon previous bounds conjectured by Feller.

Contribution

It proves that the signature of positive braid links is at least one-quarter of their first Betti number, refining the previously conjectured bound.

Findings

Signature is bounded below by one-quarter of the first Betti number.

Improves previous bound of one-eighth conjectured by Feller.

Provides a tighter relationship between link invariants and topological properties.

Abstract

We show that the signature of a positive braid link is bounded from below by one-quarter of its first Betti number. This equates to one-half of the optimal bound conjectured by Feller, who previously provided a bound of one-eighth.