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New invariants of periodic knots

Published online by Cambridge University Press:  01 September 1997

SWATEE NAIK
SWATEE NAIK
Affiliation:
Department of Mathematics, University of Nevada, Reno, NV 89557, U.S.A. e-mail: [email protected]
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Abstract

For knots in S3 we obtain new criteria for periodicity. We show that the Casson–Gordon invariants of a periodic knot are preserved under the periodic action lifted to the cyclic covers. As an application, we consider a family of knots with the Seifert form of a period 3 knot, and using Casson–Gordon invariants show that knots in this family do not have period 3. We also obtain periodicity criteria in terms of the homology groups of cyclic branched covers of S3.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 122 , Issue 2 , September 1997 , pp. 281 - 290
Copyright
Cambridge Philosophical Society 1997

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