✦ LIBER ✦
Finite Hurwitz braid group actions on sequences of Euclidean reflections
✍ Scribed by Stephen P. Humphries
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 399 KB
- Volume
- 269
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
✦ Synopsis
We prove that if r 1 , . . . , r n are Euclidean reflections corresponding to a linearly independent set of vectors, then the group r 1 , . . . , r n is finite if and only if the natural Hurwitz braid group action on such ordered sets of reflections has finite orbit and we characterise the orbits for this action. We apply 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.