Finite Hurwitz braid group actions on sequences of Euclidean reflections.
type: Item
instance of: scholarly article
title: Finite Hurwitz braid group actions on sequences of Euclidean reflections.
zbMATH Open document ID: 1040.20031
DOI: 10.1016/S0021-8693(03)00377-6
author: Stephen P. Humphries
published in: Journal of Algebra
publication date: 2003-12-04T00:00:00Z
review text: The author proves that if \(r_1,\dots, r_n\) are Euclidean reflections corresponding to a linearly independent set of vectors, then the group \(\langle r_1,\dots, r_n\rangle\) is finite if and only if the natural Hurwitz braid group action on such ordered sets of reflections has finite orbit; then he characterizes the orbits for this action. The author applies this to give a representation of the braid group on \(n\) strands onto the alternating or symmetric groups of degree \((n+ 1)^{n-2}\) (for most \(n\)) which is related to the Morse theory of polynomials, as studied by Catanese, Paluszny and Wajnryb.
Mathematics Subject Classification ID: 20F36
zbMATH DE Number: 2013029
reviewed by: Mina Teicher
describes a project that uses: Magma
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2013029