An elementary fact about unlinked braid closures

TL;DR

This paper proves a classical fact using Khovanov homology, showing that an n-strand braid whose closure is an unlink must be trivial, providing a new algebraic proof of this topological result.

Contribution

It offers the first Khovanov homology proof of the fact that unlinked braid closures imply trivial braids, connecting algebraic invariants with classical topology.

Findings

Khovanov homology confirms triviality of braids with unlink closures

Provides an algebraic proof of a classical topological fact

Strengthens the link between knot invariants and braid theory

Abstract

Let n be a positive integer. We provide a Khovanov homology proof of the following classical fact: If the closure of an n-strand braid is the n-component unlink, then the braid is trivial.