Homomorphisms of commutator subgroups of braid groups

Abstract

We give a complete classification of homomorphisms from the commutator subgroup of the braid group on $n$ strands to the braid group on $n$ strands when $n$ is at least 7. In particular, we show that each nontrivial homomorphism extends to an automorphism of the braid group on $n$ strands. This answers four questions of Vladimir Lin. Our main new tool is the theory of totally symmetric sets.

15 pages, 2 figures

References in corpus (3)

• Homomorphisms between braid groups
• Normal subgroups of the braid group and the metaconjecture of Ivanov
• Upper Bounds for Totally Symmetric Sets

Cited by in corpus (6)

• Homomorphisms between braid groups
• Small Quotients of Braid Groups
• Upper Bounds for Totally Symmetric Sets
• Homomorphisms of commutator subgroups of braid groups with small number of strings
• Endomorphisms of Artin groups of type ${\tilde{A}}_n$
• From braid groups to mapping class groups