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arXiv · 1409.4726

On the Hurwitz action on quasipositive factorizations of 3-braids

Stepan Yu. Orevkov
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Abstract

We consider the Hurwitz action on quasipositive factorizations of 3-braids. We prove that every orbit contains an element of a special form. This fact provides an algorithm of finding representatives of every orbit for a given braid. We prove also that (1) any 3-braid has a finite number of orbits; (2) a Birman-Ko-Lee positive 3-braid has a single orbit; (3) a 3-braid of algebraic length two has at most two orbits.

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Stepan Yu. Orevkov. 2014-09-16. On the Hurwitz action on quasipositive factorizations of 3-braids. https://doi.org/10.1134/s1064562415020180

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