The computation of the non-commutative generalization of the A-polynomial for the figure-eight knot

2003/01/24 by Razvan Gelca, Răzvan Gelca, Gelca, Razvan +2
Computer Science · Mathematics · #57M27 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Quantum Algebra (math.QA) #math.GT #math.QA #msc:57M27 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.math/0301287

21 pages, 12 figures

arxiv created 2003/01/24 · openalex publication_date 2003/01/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The paper contains the computation of the noncommutative A-ideal of the figure-eight knot, a noncommutative generalization of the A-polynomial. We show that if a knot has the same noncommutative A-ideal as the figure-eight knot, then all colored Kauffman brackets are the same as those of the figure-eight knot.

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