Dunfield, Nathan M. and Garoufalidis, Stavros (2004) Non-triviality of the A-polynomial for knots in S^3. Algebraic and Geometric Topology, 4 (2004). pp. 1145-1153. ISSN 1472-2747 http://resolver.caltech.edu/CaltechAUTHORS:DUNagt04
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Abstract
The A-polynomial of a knot in S^3 defines a complex plane curve associated to the set of representations of the fundamental group of the knot exterior into SL(2,C). Here, we show that a non-trivial knot in S^3 has a non-trivial A-polynomial. We deduce this from the gauge-theoretic work of Kronheimer and Mrowka on SU_2-representations of Dehn surgeries on knots in S^3. As a corollary, we show that if a conjecture connecting the colored Jones polynomials to the A-polynomial holds, then the colored Jones polynomials distinguish the unknot.
| Item Type: | Article |
|---|---|
| Additional Information: | Submitted: 13 June 2004. Accepted: 16 September 2004. Published: 1 December 2004. Both authors were partially supported by the U.S. National Science Foundation, and Dunfield was also partially supported by the Sloan Foundation. |
| Subject Keywords: | Knot, A-polynomial, character variety, Jones polynomial |
| Record Number: | CaltechAUTHORS:DUNagt04 |
| Persistent URL: | http://resolver.caltech.edu/CaltechAUTHORS:DUNagt04 |
| Alternative URL: | http://dx.doi.org/10.2140/agt.2004.4.1145 |
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. |
| ID Code: | 1013 |
| Collection: | CaltechAUTHORS |
| Deposited By: | Archive Administrator |
| Deposited On: | 29 Nov 2005 |
| Last Modified: | 26 Dec 2012 08:42 |
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