A new obstruction for ribbon-moves of 2-knots: 2-knots fibred by the punctured 3-tori and 2-knots bounded by homology spheres

Abstract

This paper gives a new obstruction for ribbon-move equivalence of 2-knots. Let $K$ and $K^{\prime }$ be 2-knots. Let $K$ and $K^{\prime }$ are ribbon-move equivalent. One corollary to our main theorem is as follows. A 2-dimensional fibered knot whose fiber is the punctured 3-dimensional torus is not ribbon-move equivalent to any 2-dimensional knot whose Seifert hypersurface is a punctured homology sphere.

27pages 5 figures

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• Introduction to high dimensional knots