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

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

2010-03-12

arxiv.org/abs/1003.2473v1

Mathematics

Geometric Topology

27pages 5 figures

Scientific paper

This paper gives a new obstruction for ribbon-move equivalence of 2-knots.
Let $K$ and $K'$ be 2-knots. Let $K$ and $K'$ 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.

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