Conway's potential function via the Gassner representation

The Gassner representation for string links

The Gassner representation of the pure braid group to $GL_n(Z[Z^n])$ can be extended to give a representation of the concordance group of $n$-strand string links to $GL_n(F)$, where $F$ is the field of quotients of $\zz[\zz^n]$, $ F = Q(t_1,...,t_n)$; this was first observed by Le Dimet. Here we present simple new perspectives on its definition, its computation, and its applications to obtain both general results and interesting family of examples.

$\mathbb{Z}_p$-模上的加斯纳表示与布劳表示

Gassner and Burau representations over $\mathbb{Z}_p$-modules

本文研究Artin辫群的Gassner与Burau表示及其模p约化，运用拓扑方法证明Gassner表示对所有n均忠实且模p忠实，并给出Burau表示模p忠实性的新证明，展望高辫群应用。

On the kernel of the Gassner representation

We study the Gassner representation of the pure braid group $P_n$ by considering its restriction to a free subgroup $F$. The kernel of the restriction is shown to lie in the subgroup $[Γ^3 F,Γ^2 F]$, sharpening a result of Lipschutz.

A Note on the Unitarity Property of the Gassner Invariant

We give a 3-page description of the Gassner invariant / representation of braids / pure braids, along with a description and a proof of its unitarity property.

Colored version for Lawrence representations

We give an explicit isomorphism between the Gassner representation and the first weight level of a representation of quantum sl(2). Then we construct and provide matrices for colored versions of the BKL representation and higher Lawrence's representations.

Quantum Relatives of Alexander Polynomial

The multivariable Conway function is generalized to oriented framed trivalent graphs equipped with additional structure (coloring). This is done via refinements of Reshetikhin-Turaev functors based on irreducible representations of quantized gl(1|1) and sl(2). The corresponding face state sum models for the generalized Conway function are presented.