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Some properties of ordinary sense slice 1-links: some answers to problem (26) of Fox

Author: Eiji Ogasa
Journal: Proc. Amer. Math. Soc. 126 (1998), 2175-2182
MSC (1991): Primary 57M25, 57Q45
MathSciNet review: 1443400
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Abstract: We prove that, for any ordinary sense slice 1-link $L$, we can define the Arf invariant, and Arf($L$)=0. We prove that, for any $m$-component 1-link $L_{1}$, there exists a $3m$-component ordinary sense slice 1-link $L_{2}$ of which $L_{1}$ is a sublink.

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Eiji Ogasa
Affiliation: Department of Mathematical Sciences, University of Tokyo, Komaba, Tokyo 153, Japan

Keywords: Ordinary sense slice 1-links, Arf invariants, $n$-dimensional knots and links, Suzuki-Terasaka diagrams, realizable 4-tuple of links
Received by editor(s): April 10, 1996
Received by editor(s) in revised form: December 27, 1996
Additional Notes: This research was partially supported by Research Fellowships of the Promotion of Science for Young Scientists.
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 1998 American Mathematical Society