Every nontrivial knot in $S^3$ has nontrivial A-polynomial
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- by Steven Boyer and Xingru Zhang PDF
- Proc. Amer. Math. Soc. 133 (2005), 2813-2815 Request permission
Abstract:
We show that every nontrivial knot in the $3$-sphere has a non-trivial $A$-polynomial.References
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- Marc Culler and Peter B. Shalen, Varieties of group representations and splittings of $3$-manifolds, Ann. of Math. (2) 117 (1983), no. 1, 109–146. MR 683804, DOI 10.2307/2006973
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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
- MR Author ID: 219677
- Email: boyer@math.uqam.ca
- Xingru Zhang
- Affiliation: Department of Mathematics, SUNY at Buffalo, Buffalo, New York, 14260-2900
- MR Author ID: 346629
- Email: xinzhang@math.buffalo.edu
- 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
- © Copyright 2005 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 133 (2005), 2813-2815
- MSC (2000): Primary 57M27, 57M25; Secondary 57M05
- DOI: https://doi.org/10.1090/S0002-9939-05-07814-7
- MathSciNet review: 2146231