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THE GENUS OF PERIODIC LINKS WITH RATIONAL QUOTIENTS

Part of: Low-dimensional topology

Published online by Cambridge University Press:  13 March 2009

SANG YOUL LEE  and
MYOUNGSOO SEO
SANG YOUL LEE
Affiliation:
Department of Mathematics, Pusan National University, Pusan 609-735, Korea (email: sangyoul@pusan.ac.kr)
MYOUNGSOO SEO*
Affiliation:
Department of Mathematics, Kyungpook National University, Daegu 702-701, Korea (email: myseo@knu.ac.kr)
*
✉For correspondence; e-mail: myseo@knu.ac.kr
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Abstract

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In this paper, we prove that if K is any periodic link in S3 whose quotient link is a 2-bridge link, then one half of the degree of the reduced Alexander polynomial, the minimal genus, the free genus and the canonical genus of K are all the same. We also give criteria to determine whether a given periodic link has a 2-bridge link quotient and some properties of this kind of periodic link.

Keywords

periodic linkgenus2-bridge linkhomogeneous link

MSC classification

Secondary: 57M25: Knots and links in $S^3$
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 79 , Issue 2 , April 2009 , pp. 273 - 284
Copyright
Copyright © Australian Mathematical Society 2009

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