On Codimension Two Ribbon Embeddings

Abstract

We consider ribbon n-knots for n\geq 2. For such knots we define a set of moves on ribbon disks, and show that any two ribbon disks for isotopic knots are related by a finite sequence of such moves and ambient isotopies. Using this we are able to prove that there is a natural geometric correspondence between ribbon n-knots and ribbon m-knots which is bijective. We also explore a diagrammatic calculus for such knots. In addition we show that for such knots, any two band presentations for the same knot are stably equivalent.

Withdrawn due to possible hole in proof

References in corpus (2)

• Exotic Statistics for Strings in 4d BF Theory
• The Classification of Spun Torus Knots

Cited by in corpus (2)

• Annulus twist and diffeomorphic 4-manifolds II
• Balloons and Hoops and their Universal Finite Type Invariant, BF Theory, and an Ultimate Alexander Invariant