منابع مشابه
Graph Theoretic Method for Determining non- Hurwitz Equivalence in the Braid Group and Symmetric group
Motivated by the problem of Hurwitz equivalence of ∆ factorization in the braid group, we address the problem of Hurwitz equivalence in the symmetric group, obtained by projecting the ∆ factorizations into Sn. We get 1Sn factorizations with transposition factors. Looking at the transpositions as the edges in a graph, we show that two factorizations are Hurwitz equivalent if and only if their gr...
متن کاملThe Hurwitz Action and Braid Group Orderings
In connection with the so-called Hurwitz action of homeomorphisms in ramified covers we define a groupoid, which we call a ramification groupoid of the 2sphere, constructed as a certain path groupoid of the universal ramified cover of the 2-sphere with finitely many marked-points. Our approach to ramified covers is based on cosheaf spaces, which are closely related to Fox’s complete spreads. A ...
متن کاملConjugacy Classes of 3-braid Group B3
In this article we describe the summit sets in B3, the smallest element in a summit set and we compute the Hilbert series corresponding to conjugacy classes. The results will be related to Birman-Menesco classification of knots with braid index three or less than three.
متن کاملHurwitz Equivalence of Braid Group Factorizations Consisting of a Semi-Frame
In this paper we prove certain Hurwitz equivalence properties in the braid group. Our main result is that every two factorizations of ∆n where the elements of the factorization are semi-frame are Hurwitz equivalent. The results of this paper are generalization of the results in [8]. We use a new presentation of the braid group, called the Birman-Ko-Lee presentation, to define the semi-frame str...
متن کاملHurwitz Equivalence of Braid Monodromies and Extremal Elliptic Surfaces
We discuss the equivalence between the categories of certain ribbon graphs and subgroups of the modular group Γ and use this equivalence to construct exponentially large families of not Hurwitz equivalent simple braid monodromy factorizations of the same element. As an application, we also obtain exponentially large families of topologically distinct algebraic objects such as extremal elliptic ...
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ژورنال
عنوان ژورنال: International Journal of Algebra and Computation
سال: 2003
ISSN: 0218-1967,1793-6500
DOI: 10.1142/s0218196703001389