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July, 2020 A Fox–Milnor theorem for the Alexander polynomial of knotted 2-spheres in $S^4$
Delphine MOUSSARD, Emmanuel WAGNER
J. Math. Soc. Japan 72(3): 891-907 (July, 2020). DOI: 10.2969/jmsj/82218221

Abstract

For knots in $S^3$, it is well-known that the Alexander polynomial of a ribbon knot factorizes as $f(t)f(t^{-1})$ for some polynomial $f(t)$. By contrast, the Alexander polynomial of a ribbon 2-knot in $S^4$ is not even symmetric in general. Via an alternative notion of ribbon 2-knots, we give a topological condition on a 2-knot that implies the factorization of the Alexander polynomial.

Citation

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Delphine MOUSSARD. Emmanuel WAGNER. "A Fox–Milnor theorem for the Alexander polynomial of knotted 2-spheres in $S^4$." J. Math. Soc. Japan 72 (3) 891 - 907, July, 2020. https://doi.org/10.2969/jmsj/82218221

Information

Received: 27 February 2019; Published: July, 2020
First available in Project Euclid: 11 May 2020

zbMATH: 07257214
MathSciNet: MR4125849
Digital Object Identifier: 10.2969/jmsj/82218221

Subjects:
Primary: 57M99
Secondary: 57Q45

Keywords: 2-knot , Alexander polynomial , Fox–Milnor theorem , knotted sphere , ribbon knot

Rights: Copyright © 2020 Mathematical Society of Japan

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Vol.72 • No. 3 • July, 2020
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