Journal of the Australian Mathematical Society

Research Article

Ribbon concordance of surface-knots via quandle cocycle invariants

J. Scott Cartera1, Masahico Saitoa2 and Shin Satoha3

a1 Department of Mathematics, University of South Alabama, Mobile AL 36688, USA, e-mail: carter@mathstat.usouthal.edu

a2 Department of Mathematics, University of South Florida, Tampa FL 33620, USA, e-mail: saito@math.usf.edu

a3 Department of Mathematics, Chiba University, Yayoi-cho 1–33, Inage-ku, Chiba 263-8522, Japan, e-mail: 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.

(Received September 24 2003)

(Revised January 12 2005)

2000 Mathematics subject classification

  • primary 57Q45;
  • secondary 57Q35

Keywords and phrases

  • surface-knot;
  • ribbon concordance;
  • quandle;
  • cocycle invariant;
  • triple point.