Skein modules and the noncommutative torus |
| |
Authors: | Charles Frohman Razvan Gelca |
| |
Institution: | Department of Mathematics, University of Iowa, Iowa City, Iowa 52242 ; Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109, and Institute of Mathematics of the Romanian Academy, Bucharest, Romania |
| |
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 -th colored Kauffman bracket of a torus knot, evaluated in the plane or in an annulus. |
| |
Keywords: | Kauffman bracket skein modules noncommutative geometry |
|
| 点击此处可从《Transactions of the American Mathematical Society》浏览原始摘要信息 |
| 点击此处可从《Transactions of the American Mathematical Society》下载免费的PDF全文 |
|