Finite orbits of Hurwitz actions on braid systems

2009/12/02 by Tetsuya Ito, Ito, Tetsuya · 1 citation
Mathematics · #20F36 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20F36

paper · pdf · doi:10.48550/arxiv.0912.0405

20 pages, 6 figures, results are improved. To appear in Osaka J. Math.

arxiv created 2010/04/19 · arxiv updated 2010/04/20

Abstract

There are natural actions of the braid groups on the products of the braid groups, called the Hurwitz action. We first study the roots of centralizers in the braid groups. By using the structure of the roots, we provide a criterion for the Hurwitz orbit become finite and give an upper bound of the size of a finite orbit in length 2 or degree 3 case.

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