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October, 2020 Linking forms, finite orthogonal groups and periodicity of links
Maciej BORODZIK, Przemysław GRABOWSKI, Adam KRÓL, Maria MARCHWICKA
J. Math. Soc. Japan 72(4): 1025-1048 (October, 2020). DOI: 10.2969/jmsj/82028202

Abstract

For a prime number $q\neq 2$ and $r>0$, we study whether there exists an isometry of order $q^r$ acting on a free $\mathbb{Z}_{p^k}$-module equipped with a scalar product. We investigate whether there exists such an isometry with no non-zero fixed points. Both questions are completely answered in this paper if $p\neq 2,q$. As an application, we refine Naik's criterion for periodicity of links in $S^3$. The periodicity criterion we obtain is effectively computable and gives concrete restrictions for periodicity of low-crossing knots.

Funding Statement

The first, third and fourth authors are supported by the National Science Center grant 2016/22/E/ST1/00040.

Citation

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Maciej BORODZIK. Przemysław GRABOWSKI. Adam KRÓL. Maria MARCHWICKA. "Linking forms, finite orthogonal groups and periodicity of links." J. Math. Soc. Japan 72 (4) 1025 - 1048, October, 2020. https://doi.org/10.2969/jmsj/82028202

Information

Received: 16 January 2019; Published: October, 2020
First available in Project Euclid: 28 July 2020

MathSciNet: MR4165922
Digital Object Identifier: 10.2969/jmsj/82028202

Subjects:
Primary: 57M25

Rights: Copyright © 2020 Mathematical Society of Japan

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Vol.72 • No. 4 • October, 2020
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