Smallest nontrivial quotients of the commutator subgroup of braid groups

Abstract

We prove that the smallest non-trivial quotients of the commutator subgroups of the braid groups are the alternating groups for n ≥ 5, proving a conjecture of Chudnovsky-Kordek-Li-Partin. Furthermore, we show that any minimal quotient map is the standard projection, composed with an automorphism of the alternating group.