Every nontrivial knot in 𝑆³ has nontrivial A-polynomial

Every nontrivial knot in $S^3$ has nontrivial A-polynomial
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Proc. Amer. Math. Soc. 133 (2005), 2813-2815

DOI: https://doi.org/10.1090/S0002-9939-05-07814-7

Published electronically: March 22, 2005

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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
P. Kronheimer and T. Mrowka, Dehn surgery, the fundamental group and $SU(2)$, preprint (available online at http://front.math.ucdavis.edu).

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Bibliographic 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
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