Towards a Diagrammatic Analogue of the Reshetikhin-turaev Link Invariants
نویسنده
چکیده
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 ZEK, 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 ZEK on the unknot. This formula is simpler than the Wheels formula of [BGRT], but the precise relationship between the two is yet unknown.
منابع مشابه
Skein Theory and Witten-reshetikhin-turaev Invariants of Links in Lens Spaces
We study the behavior of the Witten-Reshetikhin-Turaev SU(2) invariants of an arbitrary link in L(p, q) as a function of the level r− 2. They are given by
متن کاملOn the integrality of Witten-Reshetikhin-Turaev 3-manifold invariants
We prove that the SU.(2) Witten-Reshetikhin-Turaev invariant of any 3-manifold with any colored link inside at any root of unity is an algebraic integer. As a byproduct, we get a new proof of the integrality of the SO.(3) Witten-Reshetikhin-Turaev invariant for any 3-manifold with any colored link inside at any root of unity of odd order. DOI: https://doi.org/10.4171/QT/48 Posted at the Zurich ...
متن کاملVolume conjectures for the Reshetikhin-Turaev and the Turaev-Viro invariants
We conjecture that, evaluated at the root of unity exp(2π √ −1/r) instead of the standard exp(π √ −1/r), the Turaev-Viro and the Reshetikhin-Turaev invariants of a hyperbolic 3-manifold grow exponentially with growth rates respectively the hyperbolic and the complex volume of the manifold. This reveals a different asymptotic behavior of the relevant quantum invariants than that of Witten’s inva...
متن کاملReshetikhin–Turaev invariants of Seifert 3–manifolds for classical simple Lie algebras, and their asymptotic expansions
We derive explicit formulas for the Reshetikhin–Turaev invariants of all oriented Seifert manifolds associated to an arbitrary complex finite dimensional simple Lie algebra g in terms of the Seifert invariants and standard data for g. A main corollary is a determination of the full asymptotic expansions of these invariants for lens spaces in the limit of large quantum level. Our results are in ...
متن کاملOn the Spin-refined Reshetikhin-turaev Su(2) Invariants of Lens Spaces
We give an explicit presentation of the value of the spin-refined ReshetikhinTuraev SU(2) invariants of lens spaces. Using this result, we also present the value of spin-refined Turaev-Viro SU(2) invariants of lens spaces.
متن کامل