Burau maps and twisted Alexander polynomials
Anthony Conway
TL;DR
This paper introduces twisted Burau maps, extending the classical Burau representation, to compute twisted Alexander polynomials, providing a new algebraic tool for knot and braid analysis.
Contribution
The paper develops twisted Burau maps, a novel extension of the Burau representation, enabling the computation of twisted Alexander polynomials.
Findings
Twisted Burau maps effectively compute twisted Alexander polynomials.
The approach generalizes classical methods for knot invariants.
Provides a new algebraic framework for studying braid closures.
Abstract
The Burau representation of the braid group can be used to recover the Alexander polynomial of the closure of a braid. We define twisted Burau maps and use them to compute twisted Alexander polynomials.
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