Fast nielsen-thurston classification of braids

TL;DR

This paper introduces a quadratic-time algorithm for solving the reducibility problem in braid groups, significantly improving computational efficiency for classifying braids.

Contribution

It presents the first quadratic-time algorithm for Nielsen-Thurston classification of braids, addressing a longstanding computational challenge.

Findings

Algorithm runs in quadratic time for fixed braid index

Solves the reducibility problem efficiently

Advances computational methods in braid theory

Abstract

We prove the existence of an algorithm which solves the reducibility problem in braid groups and runs in quadratic time with respect to the braid length for any fixed braid index.