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The Kontsevich Integral in Book Notation | Renaud Gauthier
; | Date: |
14 Oct 2010 | Abstract: | We 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 | Services: | Forum | Review | PDF | Favorites |
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