Abstract
The Hurwitz action of the n-braid group Bn on the n-fold direct product Bmn of the m-braid group Bm is studied. We show that the isotropy subgroup of the Hurwitz group action of B3 at the triple of the standard generators of B4 has index 16, by explicitly describing a complete system of coset representatives. An application to the braided surfaces in 4-space is also given.
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