15 citations · 23 across the 4 of their papers we have counts for
8 papers
Braid groups and Iwahori-Hecke algebras
Stephen Bigelow
This article was submitted to a volume under preparation, with Benson Farb as the editor, on the topic of open problems in surface mapping class groups. The braid group B_n is the…
Homological representations of the Iwahori-Hecke algebra
Stephen Bigelow
Representations of the Iwahori-Hecke algebra of type A_{n-1} are equivalent to representations of the braid group B_n for which the generators satisfy a certain quadratic relation.…
Problems on invariants of knots and 3-manifolds
J. E. Andersen, N. Askitas, D. Bar-Natan +57
This is a list of open problems on invariants of knots and 3-manifolds with expositions of their history, background, significance, or importance. This list was made by editing ope…
Representations of braid groups
Stephen Bigelow
In this paper we survey some work on representations of given by the induced action on a homology module of some space. One of these, called the Lawrence-Krammer representati…
The Lawrence-Krammer representation
Stephen Bigelow
The Lawrence-Krammer representation of the braid groups recently came to prominence when it was shown to be faithful by myself and Krammer. It is an action of the braid group on a…
A homological definition of the Jones polynomial
Stephen Bigelow
We give a new definition of the Jones polynomial. Let L be an oriented knot or link obtained as the plat closure of a braid beta in B_{2n}. We define a covering space tilde{C} of t…