The seven-strand braid group is CAT(0)

The Deligne Complex for the Four-strand Braid Group

This paper concerns the homotopy type of hyperplane arrangements associated to infinite Coxeter groups acting as reflection groups on Cn. A long-standing conjecture states that the complement of such an arrangement should be aspherical. Some partial results on this conjecture were previously obtained by the author and M. Davis. In this paper, we extend those results to another class of Coxeter ...

The Algebra of Strand Splitting Ii: a Presentation for the Braid Group on One Strand

In [3], we give descriptions of a braided version BV of Thompson’s group V as well as a group B̂V that contains BV as a subgroup and that is somewhat easier to work with. The paper [3] contains both geometric and algebraic descriptions of these two groups and shows that for each group the two descriptions are of isomorphic groups. An infinite presentation for B̂V is also given in [3]. The current...

The Braid Group of Z

We define quasi-Garside groups and prove a theorem about them parallel to Garside’s result on the word problem for the usual braid groups. We introduce a group which we call the braid group B of Zn, and which bears some resemblance to mapping class groups. We prove that B is a quasi-Garside group. We give a ‘small presentation’ for B.

Braid Group Cryptography

In the last decade, a number of public key cryptosystems based on combinatorial group theoretic problems in braid groups have been proposed. We survey these cryptosystems and some known attacks on them. This survey includes: Basic facts on braid groups and on the Garside normal form of its elements, some known algorithms for solving the word problem in the braid group, the major public-key cryp...

Derivative Varieties and the Pure Braid Group