Finite orbits of Hurwitz actions on braid systems

Mathematics – Group Theory

Scientific paper

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

Scientific paper

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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