Splitting numbers of links and the four-genus

TL;DR

This paper establishes a new bound on the splitting number of links using the four-genus of related knots, advancing understanding of link splitting complexity.

Contribution

It introduces a novel bound relating the splitting number of links to the four-genus of associated knots, providing new insights into link topology.

Findings

Bound on splitting number in terms of four-genus

Relation between crossing changes and knot invariants

Enhanced tools for analyzing link splitting complexity

Abstract

The splitting number of a link is the minimum number of crossing changes between distinct components that is required to convert the link into a split link. We provide a bound on the splitting number in terms of the four-genus of related knots.