Simple Braids

TL;DR

This paper investigates a specific subset of positive braids, providing algebraic and geometric characterizations, and describing their canonical forms and conjugacy classes, with implications for understanding unlinks.

Contribution

It introduces new algebraic and geometric characterizations of a subset of positive braids and describes their canonical forms and conjugacy classes.

Findings

Characterization of positive braids with unlink closures

Canonical forms of these braids and their conjugacy classes

Connection between algebraic properties and geometric unlink structures

Abstract

We study a subset of square free positive braids and we give a few algebraic characterizations of them and one geometric characterization: the set of positive braids whose closures are unlinks. We describe canonical forms of these braids and of their conjugacy classes.