CaltechAUTHORS
  A Caltech Library Service

Non-triviality of the A-polynomial for knots in S³

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. https://resolver.caltech.edu/CaltechAUTHORS:DUNagt04

[img]
Preview
PDF - Published Version
See Usage Policy.

136Kb
[img] PDF - Submitted Version
See Usage Policy.

68Kb

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:DUNagt04

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
Related URLs:
URLURL TypeDescription
https://doi.org/10.2140/agt.2004.4.1145DOIArticle
https://arxiv.org/abs/math/0405353arXivDiscussion Paper
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.
Funders:
Funding AgencyGrant Number
NSFUNSPECIFIED
Alfred P. Sloan FoundationUNSPECIFIED
Subject Keywords:Knot, A-polynomial, character variety, Jones polynomial
Issue or Number:2004
Classification Code:AMS subject classification. Primary: 57M25, 57M27. Secondary: 57M50.
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:19 May 2020 16:13

Repository Staff Only: item control page