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Ribbon concordance of surface-knots via quandle cocycle invariants

Part of: PL-topology

Published online by Cambridge University Press:  09 April 2009

J. Scott Carter ,
Masahico Saito  and
Shin Satoh
J. Scott Carter
Affiliation:
Department of Mathematics, University of South Alabama, Mobile AL 36688, USA, e-mail: carter@mathstat.usouthal.edu
Masahico Saito
Affiliation:
Department of Mathematics, University of South Florida, Tampa FL 33620, USA, e-mail: saito@math.usf.edu
Shin Satoh
Affiliation:
Department of Mathematics, Chiba University, Yayoi-cho 1–33, Inage-ku, Chiba 263-8522, Japan, e-mail: satoh@math.s.chiba-u.ac.jp
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Abstract

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We give necessary conditions of a surface-knot to be ribbon concordant to another, by introducing a new variant of the cocycle invariant of surface-knots in addition to using the invariant already known. We demonstrate that twist-spins of some torus knots are not ribbon concordant to their orientation reversed images.

Keywords

surface-knotribbon concordancequandlecocycle invarianttriple point.

MSC classification

Secondary: 57Q45: Knots and links (in high dimensions) 57Q35: Embeddings and immersions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 80 , Issue 1 , February 2006 , pp. 131 - 147
Copyright
Copyright © Australian Mathematical Society 2006

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