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.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2019
- DOI:
- 10.48550/arXiv.1910.06941
- arXiv:
- arXiv:1910.06941
- Bibcode:
- 2019arXiv191006941K
- Keywords:
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- Mathematics - Geometric Topology;
- Mathematics - Group Theory
- E-Print:
- 15 pages, 2 figures