On Codimension Two Ribbon Embeddings

Blake Winter

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arXiv · 0904.0684

On Codimension Two Ribbon Embeddings

Blake Winter

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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.

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BibTeX RIS

Blake Winter. 2009-04-06. On Codimension Two Ribbon Embeddings. https://arxiv.org/abs/0904.0684

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