Towards a Diagrammatic Analogue of the Reshetikhin-Turaev Link Invariants

Abstract

By considering spaces of directed Jacobi diagrams, we construct a diagrammatic version of the Etingof-Kazhdan quantization of complex semisimple Lie algebras. This diagrammatic quantization is used to provide a construction of a directed version of the Kontsevich integral, denoted $Z_{E}K$, in a way which is analogous to the construction of the Reshetikhin-Turaev invariants from the R-matrices of the Drinfel'd-Jimbo quantum groups. Based on this analogy, we conjecture (and prove in a restricted sense) a formula for the value of the invariant $Z_{E}K$ on the unknot. This formula is simpler than the Wheels formula of [BGRT], but the precise relationship between the two is yet unknown.

92 pages, Hebrew U. Ph.D. thesis

References in corpus (5)

• Quantization of Lie bialgebras, V
• The Fundamental Theorem of Vassiliev Invariants
• The number of primitive Vassiliev invariants up to degree 12
• Twisting invariance of link polynomials derived from ribbon quasi-Hopf algebras
• Wheeling: A diagrammatic analogue of the Duflo isomorphism

Cited by in corpus (5)

• Finite Type Invariants of w-Knotted Objects I: w-Knots and the Alexander Polynomial
• Finite Type Invariants of w-Knotted Objects: From Alexander to Kashiwara and Vergne
• Combinatorial Formulas for Classical Lie Weight Systems on Arrow Diagrams
• Some Dimensions of Spaces of Finite Type Invariants of Virtual Knots
• Classification of Flat Virtual Pure Tangles