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Skein Modules and the Noncommutative Torus

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arxiv math/9806107 v1 pith:C5PNIWA2 submitted 1998-06-19 math.QA math.GTmath.OA

Charles Frohman , Razvan Gelca This is my paper · ORCID
classification math.QAmath.GTmath.OA
keywords moduleskeintorusbracketkauffmancylindernoncommutativeanalyze
verification ladder T0 review T1 audit T2 compute T3 formal

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We show that the Kauffman bracket skein module of a cylinder over the torus embeds as a subalgebra of the noncommutative torus. Using this we derive nice formulas for the Jones-Wenzl idempotents and analyze the structure of the Kauffman bracket skein module of the unknot as a module over the Kauffman bracket skein module of a cylinder over the torus.

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  1. Chebyshev polynomials and Gram determinants from the M\"obius band

    math.GT 2025-04 reject novelty 5.0 of 10

    The paper proves that the (2^k-1)th second-kind Chebyshev polynomial factors as a product of first-kind Chebyshev polynomials, restates two Gram determinant conjectures, and proves a supporting divisibility factor tha...

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