The Multivariable Alexander Polynomial for a Closed Braid
H.R.Morton
TL;DR
This paper introduces a straightforward multivariable version of the reduced Burau matrix for braids, enabling direct computation of the multivariable Alexander polynomial of the braid's closure.
Contribution
It presents a novel multivariable matrix construction that simplifies the calculation of the Alexander polynomial for closed braids.
Findings
Multivariable Alexander polynomial can be computed directly from the new matrix.
The method applies to any braid, broadening computational tools in knot theory.
Simplifies existing approaches to calculating invariants of braid closures.
Abstract
A simple multivariable version of the reduced Burau matrix is constructed for any braid. It is shown how the multivariable Alexander polynomial for the closure of the braid can be found directly from this matrix.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · Nonlinear Waves and Solitons