Homomorphisms of commutator subgroups of braid groups
Geometric Topology
2022-03-14 v2 Group Theory
Abstract
We give a complete classification of homomorphisms from the commutator subgroup of the braid group on strands to the braid group on strands when is at least 7. In particular, we show that each nontrivial homomorphism extends to an automorphism of the braid group on strands. This answers four questions of Vladimir Lin. Our main new tool is the theory of totally symmetric sets.
Cite
@article{arxiv.1910.06941,
title = {Homomorphisms of commutator subgroups of braid groups},
author = {Kevin Kordek and Dan Margalit},
journal= {arXiv preprint arXiv:1910.06941},
year = {2022}
}
Comments
15 pages, 2 figures