Journal article
Skein modules and the noncommutative torus
Transactions of the American Mathematical Society, Vol.352(10), pp.4877-4888
10/01/2000
DOI: 10.1090/S0002-9947-00-02512-5
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 idempotents 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.
Details
- Title: Subtitle
- Skein modules and the noncommutative torus
- Creators
- Charles Frohman - University of Iowa, MathematicsRăzvan Gelca - Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109, and Institute of Mathematics of the Romanian Academy, Bucharest, Romania
- Resource Type
- Journal article
- Publication Details
- Transactions of the American Mathematical Society, Vol.352(10), pp.4877-4888
- DOI
- 10.1090/S0002-9947-00-02512-5
- ISSN
- 0002-9947
- eISSN
- 1088-6850
- Publisher
- American Mathematical Society
- Number of pages
- 12
- Language
- English
- Date published
- 10/01/2000
- Academic Unit
- Mathematics
- Record Identifier
- 9983985947502771
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