منابع مشابه
On the Linearity of Braid Groups
To understand what a braid group is, it is easiest to visualize a braid. Consider n strands, all parallel. Consider taking the ith strand and crossing it over the i+ 1th strand. This is an example of a braid. In general, a braid is any sequence of crossings of the bands, provided none of the bands are selfcrossing. For instance, a loop, or a band which forms a loop in the middle, is not a braid...
متن کاملBraid Pictures for Artin Groups
We define the braid groups of a two-dimensional orbifold and introduce conventions for drawing braid pictures. We use these to realize the Artin groups associated to the spherical Coxeter diagrams An, Bn = Cn and Dn and the affine diagrams Ãn, B̃n, C̃n and D̃n as subgroups of the braid groups of various simple orbifolds. The cases Dn, B̃n, C̃n and D̃n are new. In each case the Artin group is a normal...
متن کاملArtin Braid Groups and Homotopy Groups
We study the Brunnian subgroups and the boundary Brunnian subgroups of the Artin braid groups. The general higher homotopy groups of the sphere are given by mirror symmetric elements in the quotient groups of the Artin braid groups modulo the boundary Brunnian braids, as well as given as a summand of the center of the quotient groups of Artin pure braid groups modulo boundary Brunnian braids. T...
متن کاملArtin Covers of the Braid Groups
Computation of fundamental groups of Galois covers recently led to the construction and analysis of Coxeter covers of the symmetric groups [RTV]. In this paper we consider analog covers of Artin’s braid groups, and completely describe the induced geometric extensions of the braid group.
متن کاملLinearity of Artin Groups of Finite Type
Recent results on the linearity of braid groups are extended in two ways. We generalize the Lawrence Krammer representation as well as Krammer’s faithfulness proof for this linear representation to Artin groups of finite type.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2003
ISSN: 0021-8693
DOI: 10.1016/s0021-8693(03)00327-2