Yan Loi Wong

Configurations, braids, and homotopy groups

The main results of this article are certain connections between braid groups and the homotopy groups of the 2-sphere. The connections are given in terms of Brunnian braids over the disk and over the 2-sphere. The techniques arise from the natural structure of simplicial and ∆-structures on fundamental groups of configuration spaces.

Braids : introductory lectures on braids, configurations and their applications

Tutorial on the Braid Groups Simplicial Objects and Homotopy Groups Introduction to Configuration Spaces and Their Applications Braids and Magnetic Fields Configuration Spaces, Braids, and Robotics Braid Group Cryptography.

Finite quotients of the automorphism group of a free group

The automorphism group AutFn of a free group Fn of rank n acts on the product of n copies of a group G by substituting n elements of G into the words defining an automorphism of the free group. This gives rise to an antihomomorphism from AutFnto a permutation group. We determine this antihomomorphic image of AutFn when G is the semidirect product Zp x Zq

ON QUOTIENTS OF BRAID GROUPS

ABSTRACT. Let G be the group ℤ[t, t −1] x ℤ. By studying the action of the braid group Bn on the set Gn , we obtain representations of Bn into a wreath product of the symmetric group and the general linear group over ℤ[t, t −1]. This in particular recovers the Burau representation of the braid group. Furthermore, some quotients of the braid group are obtained by using the representations found.

On the Pass-equivalence of links

We give a simple geometric proof that the Jones polynomial at the value i of an oriented link is invariant under pass-equivalence.