On Codimension Two Ribbon Embeddings

Blake Winter

On Codimension Two Ribbon Embeddings

Geometric Topology 2015-09-04 v9

Authors: Blake Winter

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.

Keywords

knot theory

Cite

@article{arxiv.0904.0684,
  title  = {On Codimension Two Ribbon Embeddings},
  author = {Blake Winter},
  journal= {arXiv preprint arXiv:0904.0684},
  year   = {2015}
}

Comments

Withdrawn due to possible hole in proof

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