English

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 nn strands to the braid group on nn strands when nn is at least 7. In particular, we show that each nontrivial homomorphism extends to an automorphism of the braid group on nn strands. This answers four questions of Vladimir Lin. Our main new tool is the theory of totally symmetric sets.

Keywords

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