Homomorphisms of commutator subgroups of braid groups

Kevin Kordek; Dan Margalit

doi:10.1112/blms.12560

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arXiv · 1910.06941

Homomorphisms of commutator subgroups of braid groups

Kevin Kordek·Dan Margalit

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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.

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Kevin Kordek, Dan Margalit. 2019-10-15. Homomorphisms of commutator subgroups of braid groups. https://doi.org/10.1112/blms.12560

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