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Hurwitz action on tuples of Euclidean reflections

Jean Michel
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Abstract

We show that if a tuple of Euclidean reflections has a finite orbit under the Hurwitz action of the Artin braid group, then the group generated by these reflections is finite. Humphries has published a similar statement but his proof is irremediably flawed. At the same time as correcting his proof, our proof is much simpler that Dubrovin and Mazocco's proof for triples of reflections.

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Jean Michel. 2004-10-13. Hurwitz action on tuples of Euclidean reflections. https://arxiv.org/abs/math/0410313

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