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


Alexander polynomials of doubly primitive knots

Authors: Kazuhiro Ichihara, Toshio Saito and Masakazu Teragaito
Journal: Proc. Amer. Math. Soc. 135 (2007), 605-615
MSC (2000): Primary 57M25
Published electronically: August 10, 2006
MathSciNet review: 2255308
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Abstract: We give a formula for Alexander polynomials of doubly primitive knots. This also gives a practical algorithm to determine the genus of any doubly primitive knot.

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Additional Information

Kazuhiro Ichihara
Affiliation: College of General Education, Osaka Sangyo University, Nakagaito 3-1-1, Daito, Osaka 574-8530, Japan

Toshio Saito
Affiliation: Graduate School of Humanities and Sciences, Nara Women’s University, Kitauoyanishi-machi, Nara 630-8506, Japan

Masakazu Teragaito
Affiliation: Department of Mathematics and Mathematics Education, Hiroshima University, Kagamiyama 1-1-1, Higashi-hiroshima, Japan 739-8524.

PII: S 0002-9939(06)08496-6
Keywords: Doubly primitive knot, Alexander polynomial
Received by editor(s): June 21, 2005
Received by editor(s) in revised form: September 13, 2005
Published electronically: August 10, 2006
Additional Notes: The second author was supported by the 21st Century COE program \lq\lq Towards a New Basic Science; Depth and Synthesis\rq\rq, Osaka University.
The third author was partially supported by the Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C), 16540071.
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.