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Strong periodicity of links and the coefficients of the Conway polynomial


Author: Nafaa Chbili
Journal: Proc. Amer. Math. Soc. 136 (2008), 2217-2224
MSC (2000): Primary 57M25
DOI: https://doi.org/10.1090/S0002-9939-08-09266-6
Published electronically: February 7, 2008
MathSciNet review: 2383528
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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$.


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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
Email: chbili@sci.osaka-cu.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-08-09266-6
Keywords: Strongly periodic links, equivariant crossing change, Conway polynomial.
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
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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