Skein modules and the noncommutative torus

Charles Frohman, Räzvan Gelca

Research output: Contribution to journalArticlepeer-review

65 Scopus citations

Abstract

We prove that the Kauffman bracket skein algebra of the cylinder over a torus is a canonical subalgebra of the noncommutative torus. The proof is based on Chebyshev polynomials. As an application, we describe the structure of the Kauffman bracket skein module of a solid torus as a module over the algebra of the cylinder over a torus, and recover a result of Hoste and Przytycki about the skein module of a lens space. We establish simple formulas for Jones-Wenzl idempotcnts in the skein algebra of a cylinder over a torus, and give a straightforward computation of the n-th colored Kauffman bracket of a torus knot, evaluated in the plane or in an annulus.

Original languageEnglish
Pages (from-to)4877-4888
Number of pages12
JournalTransactions of the American Mathematical Society
Volume352
Issue number10
DOIs
StatePublished - 2000

Keywords

  • Kauffraan bracket
  • Noncommutative geometry
  • Skein modules

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