Automorphism group of the commutator subgroup of the braid group

TL;DR

This paper proves that for braid groups with at least four strands, the automorphism group of their commutator subgroup is identical to that of the entire braid group, resolving a question in algebraic topology.

Contribution

It establishes the equality of automorphism groups for the commutator subgroup and the entire braid group for all n ≥ 4, answering a previously open question.

Findings

Aut(B'_n) = Aut(B_n) for n ≥ 4

Provides a complete characterization of automorphisms of the commutator subgroup

Answers a longstanding question in the theory of braid groups

Abstract

Let $B'_n$ be the commutator subgroup of the braid group $B_n$. We prove that $Aut(B'_n)=Aut(B_n)$ for $n\ge4$. This answers a question asked by Vladimir Lin.