2 00 5 Braid Family Representatives

Braid Family Representatives

After defining reduced minimum braid word and criteria for a braid family representative , different braid family representatives are derived, and a correspondence between them and families of knots and links given in Conway notation is established .

ar X iv : m at h / 02 10 26 0 v 1 [ m at h . Q A ] 1 7 O ct 2 00 2 On representations of braid groups determined by directed graphs 1

We show that any Markov L-coalgebra, i.e. a k-vector space equipped with two coproducts representing a directed graph yields a solution of the Yang-Baxter equation and thus a representation of braid groups. If the directed graph is equipped with a family of probability vectors then such family yields also a representation of braid groups. We end by a generalisation of these construction to any ...

. G T ] 1 9 A ug 2 00 5 Braid Groups of the Sun Graph

In this article we calculate the n-string braid groups of certain noncontractible graphs. We use techniques from the work of A. Abrams, F. Connolly and M. Doig combined with Van Kampen’s Theorem to prove these results.

ar X iv : 0 71 1 . 23 72 v 1 [ m at h . G R ] 1 5 N ov 2 00 7 Braid groups and Artin groups

2 00 5 the N - Eigenvalue Problem and Two Applications

We consider the classification problem for compact Lie groups G ⊂ U(n) which are generated by a single conjugacy class with a fixed number N of distinct eigenvalues. We give an explicit classification when N = 3, and apply this to extract information about Galois representations and braid group representations.