The congruence subgroup problem for braid groups: Thurston's proof

TL;DR

This paper presents Thurston's unpublished proof demonstrating that pure braid groups possess the congruence subgroup property, a significant result in understanding their algebraic structure.

Contribution

It provides the first detailed exposition of Thurston's proof that pure braid groups have the congruence subgroup property.

Findings

Pure braid groups have the congruence subgroup property.

Thurston's proof confirms a long-standing conjecture.

The result impacts the understanding of braid group representations.

Abstract

In this article we present an unpublished proof of W. Thurston that pure braid groups have the congruence subgroup property.