Thurston's Operations on the Braid Groups

TL;DR

This paper investigates Thurston's automaton on braid groups through binary operations, exploring their structure and connections within a skew lattice framework to deepen understanding of braid group automorphisms.

Contribution

It introduces and analyzes binary operations derived from Thurston's automaton, revealing their algebraic properties and interrelations within a skew lattice context.

Findings

Identified binary operations from Thurston's automaton

Established connections between these operations in a skew lattice framework

Enhanced understanding of automorphism structures in braid groups

Abstract

In this paper we study Thurston's automaton on the braid groups via binary operations. These binary operations are obtained from the construction of this automaton. We study these operations and find some connections between them in a "skew lattice" spirit.