The A-polynomial from the noncommutative viewpoint

1998/12/08 by Charles Frohman, Răzvan Gelca, Razvan Gelca +5 · 2 citations
Mathematics · #46L87 #57M99 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #math.GT #math.OA #math.QA #msc:46L87 #msc:57M99

paper · pdf · doi:10.48550/arxiv.math/9812048

13 pages, Latex, 3 diagrams, epsfig

arxiv created 1998/12/08 · openalex publication_date 1998/12/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop an invariant of knots that depends on a complex parameter t, describing a left ideal in the noncommutative torus. When the parameter is set equal to -1 we recover the A-polynomial of the knot. We relate the invariant to the colored Jones polynomials of the knot.

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• An effective proof of finiteness for Kauffman bracket skein modules
• Parabolic skein modules

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