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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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.
|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|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Archive Administrator|
|Deposited On:||29 Nov 2005|
|Last Modified:||26 Dec 2012 08:42|
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