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29 March 2024
 
  » arxiv » 1010.2814

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The Kontsevich Integral in Book Notation
Renaud Gauthier ;
Date 14 Oct 2010
AbstractWe introduce a matrix representation of a chord on a tangle which leads us to representing tangle chord diagrams as stacks of matrices that we call books. We show that band sum moves, Reidemeister moves as well as orientation changes are implemented on widetilde{Z}_f - a framed link invariant constructed from the Kontsevich integral that’s well-behaved under band sum moves - by similarity matrix transformations. We prove that being given the bare framed Kontsevich integral Z_f(L) in book notation for some unknown link L, we can determine what the link L is, as well as the projection of Z_f(L) in the original completed algebra of chord diagrams.
Source arXiv, 1010.2814
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