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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Every nontrivial knot in $S^3$ has nontrivial A-polynomial


Authors: Steven Boyer and Xingru Zhang
Journal: Proc. Amer. Math. Soc. 133 (2005), 2813-2815
MSC (2000): Primary 57M27, 57M25; Secondary 57M05
Published electronically: March 22, 2005
MathSciNet review: 2146231
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Abstract: We show that every nontrivial knot in the $3$-sphere has a non-trivial $A$-polynomial.


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Additional Information

Steven Boyer
Affiliation: Département de Mathématiques, Université du Québec à Montréal, P.O. Box 8888, Centre-ville, Montréal, Québec, Canada H3C 3P8
Email: boyer@math.uqam.ca

Xingru Zhang
Affiliation: Department of Mathematics, SUNY at Buffalo, Buffalo, New York, 14260-2900
Email: xinzhang@math.buffalo.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07814-7
PII: S 0002-9939(05)07814-7
Keywords: $A$-polynomial, character variety, knot
Received by editor(s): May 4, 2004
Received by editor(s) in revised form: May 12, 2004
Published electronically: March 22, 2005
Additional Notes: The first author was supported in part by NSERC grant RGPIN-9446 and FQRNT grant PR-88174.
The second author was supported in part by NSF grant DMS 0204428.
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2005 American Mathematical Society