Strong periodicity of links and the coefficients of the Conway polynomial
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Abstract:
Przytycki and Sokolov proved that a three-manifold admits a semi-free action of the finite cyclic group of order $p$ with a circle as the set of fixed points if and only if $M$ is obtained from the three-sphere by surgery along a strongly $p$-periodic link $L$. Moreover, if the quotient three-manifold is an integral homology sphere, then we may assume that $L$ is orbitally separated. This paper studies the behavior of the coefficients of the Conway polynomial of such a link. Namely, we prove that if $L$ is a strongly $p$-periodic orbitally separated link and $p$ is an odd prime, then the coefficient $a_{2i}(L)$ is congruent to zero modulo $p$ for all $i$ such that $2i<p-1$.References
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Additional Information
- Nafaa Chbili
- Affiliation: Osaka City University Advanced Mathematical Institute, Sugimoto 3-3-138, Sumiyoshi-ku 558 8585 Osaka, Japan
- MR Author ID: 623443
- Email: chbili@sci.osaka-cu.ac.jp
- Received by editor(s): August 31, 2006
- Published electronically: February 7, 2008
- Additional Notes: The author was supported by a fellowship from the COE program “Constitution of wide-angle mathematical basis focused on knots”, Osaka City University.
- Communicated by: Daniel Ruberman
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 2217-2224
- MSC (2000): Primary 57M25
- DOI: https://doi.org/10.1090/S0002-9939-08-09266-6
- MathSciNet review: 2383528