Volume 4, issue 2 (2004)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 19
Issue 2, 533–1078
Issue 1, 1–532

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Other MSP Journals
Non-triviality of the $A$–polynomial for knots in $S^3$

Nathan M Dunfield and Stavros Garoufalidis

Algebraic & Geometric Topology 4 (2004) 1145–1153

arXiv: math.GT/0405353


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 SL2. 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.

knot, $A$–polynomial, character variety, Jones polynomial
Mathematical Subject Classification 2000
Primary: 57M25, 57M27
Secondary: 57M50
Forward citations
Received: 13 June 2004
Accepted: 16 September 2004
Published: 1 December 2004
Nathan M Dunfield
Mathematics 253-37
California Institute of Technology
Pasadena CA 91125
Stavros Garoufalidis
School of Mathematics
Georgia Institute of Technology
Atlanta GA 30332-0160