Units of the String Link Monoids

TL;DR

This paper proves that the group of n-strand braids is isomorphic to the group of units in the monoid of n-strand string links, establishing a fundamental algebraic connection between these structures.

Contribution

It demonstrates that viewing geometric braids as string links induces an isomorphism with the units of the string link monoid, clarifying their algebraic relationship.

Findings

The braid group is isomorphic to the group of units in the string link monoid.

The isomorphism is induced by the geometric interpretation of braids as string links.

This result bridges the algebraic structures of braids and string links.

Abstract

We show that the map obtained by viewing a geometric (ie. representative) braid as a string link induces an isomorphism of the n-strand braid group onto the group of units of the n-strand string link monoid.