a1 Department of Mathematics, University of South Alabama, Mobile AL 36688, USA, e-mail: firstname.lastname@example.org
a2 Department of Mathematics, University of South Florida, Tampa FL 33620, USA, e-mail: email@example.com
a3 Department of Mathematics, Chiba University, Yayoi-cho 1–33, Inage-ku, Chiba 263-8522, Japan, e-mail: firstname.lastname@example.org
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.
(Received September 24 2003)
(Revised January 12 2005)
2000 Mathematics subject classification
Keywords and phrases