Dunfield, Nathan M. and Garoufalidis, Stavros (2004) Non-triviality of the A-polynomial for knots in S³. Algebraic and Geometric Topology, 4 (2004). pp. 1145-1153. ISSN 1472-2747. doi:10.2140/agt.2004.4.1145. https://resolver.caltech.edu/CaltechAUTHORS:DUNagt04
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Abstract
The A-polynomial of a knot in S³ defines a complex plane curve associated to the set of representations of the fundamental group of the knot exterior into SL₂C. Here, we show that a non-trivial knot in S³ has a non-trivial A-polynomial. We deduce this from the gauge-theoretic work of Kronheimer and Mrowka on SU₂-representations of Dehn surgeries on knots in S³. 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 | |||||||||
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| 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. | |||||||||
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| Subject Keywords: | Knot, A-polynomial, character variety, Jones polynomial | |||||||||
| Issue or Number: | 2004 | |||||||||
| Classification Code: | AMS subject classification. Primary: 57M25, 57M27. Secondary: 57M50. | |||||||||
| DOI: | 10.2140/agt.2004.4.1145 | |||||||||
| Record Number: | CaltechAUTHORS:DUNagt04 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:DUNagt04 | |||||||||
| 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: | 08 Nov 2021 19:06 |
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