On 3-strand singular pure braid group

Derivative Varieties and the Pure Braid Group

Geometric Presentations for the Pure Braid Group

We give several new positive finite presentations for the pure braid group that are easy to remember and simple in form. All of our presentations involve a metric on the punctured disc so that the punctures are arranged “convexly”, which is why we describe them as geometric presentations. Motivated by a presentation for the full braid group that we call the “rotation presentation”, we introduce...

On the Singular Braid Monoid

Garside’s results and the existence of the greedy normal form for braids are shown to be true for the singular braid monoid. An analog of the presentation of J. S. Birman, K. H. Ko, and S. J. Lee for the classical braid group is also obtained for this monoid.

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 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 ...