Journal article
The A-polynomial from the noncommutative viewpoint
Transactions of the American Mathematical Society, Vol.354(2), pp.735-747
2002
DOI: 10.1090/S0002-9947-01-02889-6
Abstract
The paper introduces a noncommutative generalization of the A-polynomial of a knot. This is done using the Kauffman bracket skein module of the knot complement, and is based on the relationship between skein modules and character varieties. The construction is possible because the Kauffman bracket skein algebra of the cylinder over the torus is a subalgebra of the noncommutative torus. The generalized version of the A-polynomial, called the noncommutative A-ideal, consists of a finitely generated ideal of polynomials in the quantum plane. Some properties of the noncommutative A-ideal and its relationships with the A-polynomial and the Jones polynomial are discussed. The paper concludes with the description of the examples of the unknot, and the right- and left-handed trefoil knots.
Details
- Title: Subtitle
- The A-polynomial from the noncommutative viewpoint
- Creators
- Charles FrohmanRǎzvan GelcaWalter Lofaro
- Resource Type
- Journal article
- Publication Details
- Transactions of the American Mathematical Society, Vol.354(2), pp.735-747
- DOI
- 10.1090/S0002-9947-01-02889-6
- ISSN
- 0002-9947
- eISSN
- 1088-6850
- Publisher
- American Mathematical Society
- Language
- English
- Date published
- 2002
- Academic Unit
- Mathematics
- Record Identifier
- 9983986088302771
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