ISOTROPY SUBGROUP OF HURWITZ ACTION OF THE 3-BRAID GROUP ON THE BRAID SYSTEMS

摘要

The Hurwitz action of the n-braid group B-n on the n-fold direct product B-m(n) of the m-braid group B-m is studied. We show that the isotropy subgroup of the Hurwitz group action of B-3 at the triple of the standard generators of B-4 has index 16, by explicitly describing a complete system of coset representatives. An application to the braided surfaces in 4-space is also given.