On Codimension Two Ribbon Embeddings

Details On Codimension Two Ribbon Embeddings On Codimension Two Ribbon Embeddings

2009-04-06

arxiv.org/abs/0904.0684v9

Mathematics

Geometric Topology

Significantly simplified the main proof

Scientific paper

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.

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