The Kontsevich Integral in Book Notation

2010/10/14 by Gauthier, Renaud
#FOS: Mathematics #Geometric Topology (math.GT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1010.2814

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 \widetildeZ_f - a framed link invariant constructed from the Kontsevich integral that's well-behaved under band sum moves - by matrix congruences. 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.

Related

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• The Generating Functional of the Kontsevich Integral and its Derivation\n as a Holonomy
• The universal Vassiliev-Kontsevich invariant for framed oriented links
• Linking coefficients and the Kontsevich integral
• The lines of the Kontsevich integral and Rozansky's rationality conjecture