Abstract

A 2-variable matrix B in GL_n(Z[u^±1,v^±1]) is defined for any n-string link, generalizing the Burau matrix of an n-braid. The specialization u = 1,v = t⁻¹ recovers the generalized Burau matrix recently defined by X. S. Lin, F. Tian and Z. Wang using probabilistic methods. The specialization u = t⁻¹,v = 1 results in a matrix with a natural algebraic interpretation, and one that yields homological information about the complement of the closed string link.

Authors