The braid group Bn is not a quotient of a quasi-Coxeter interval group of type Dn

2026/07/15 by Barbara Baumeister, Luis Paris, Sarah Rees
#math.GR

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Abstract

We prove that, for n ≥ 5, an interval group associated with a proper quasi-Coxeter element of the Coxeter group of type D_n admits no surjective homomorphism onto the braid group on n strands. In particular, this provides an alternative proof that such a group is not isomorphic to the Artin group of type D_n. The proof relies on techniques from the theory of mapping class groups, and a large part of the paper provides an exposition of this theory for non-specialists.

Citations

• Curves on 2-manifolds and isotopies

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