Ribbon concordance of surface-knots via quandle cocycle invariants

J. Aust. Math. Soc. 80 (2006), 131-147

Ribbon concordance of surface-knots via quandle cocycle invariants

J. Scott Carter
Department of Mathematics
University of South Alabama
Mobile AL 36688
USA
carter@mathstat.usouthal.edu

Masahico Saito
Department of Mathematics
University of South Florida
Tampa FL 33620
USA
saito@math.usf.edu

and

Shin Satoh
Department of Mathematics
Chiba University
Yayoi-cho 1-33
Inage-ku, Chiba 263-8522
Japan
satoh@math.s.chiba-u.ac.jp

Abstract

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.

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