On the Hurwitz action on quasipositive factorizations of 3-braids

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.

7 pages, 4 figures

References in corpus (1)

• Algorithmic recognition of quasipositive braids of algebraic length two

Cited by in corpus (1)

• Criterion of Hurwitz equivalence for quasipositive factorizations of 3-braids