ar X iv : q - a lg / 9 70 30 25 v 3 2 6 A pr 1 99 8 WHEELS , WHEELING , AND THE KONTSEVICH INTEGRAL OF THE UNKNOT
نویسنده
چکیده
We conjecture an exact formula for the Kontsevich integral of the unknot, and also conjecture a formula (also conjectured independently by Deligne [De]) for the relation between the two natural products on the space of Chinese characters. The two formulas use the related notions of “Wheels” and “Wheeling”. We prove these formulas ‘on the level of Lie algebras’ using standard techniques from the theory of Vassiliev invariants and the theory of Lie algebras.
منابع مشابه
Wheels, Wheeling, and the Kontsevich Integral of the Unknot
We conjecture an exact formula for the Kontsevich integral of the unknot, and also conjecture a formula (also conjectured independently by Deligne [De]) for the relation between the two natural products on the space of uni-trivalent diagrams. The two formulas use the related notions of “Wheels” and “Wheeling”. We prove these formulas ‘on the level of Lie algebras’ using standard techniques from...
متن کاملWheels , Wheeling , and the Kontsevich Integral of the Unknot 3
We mix together the Kontsevich integral, chord diagrams, Chinese characters, the Reshetikhin-Turaev knot invariants, the Poincare-Birkhoo-Witt theorem, the Harish-Chandra isomorphism, the Duuo isomorphism, the Kirillov formula and some minor Fourier-analysis computations. This enables us to make an intelligent guess for an exact formula for the Kontsevich integral of the unknot, and to conjectu...
متن کاملTwo Applications of Elementary Knot Theory to Lie Algebras and Vassiliev Invariants
Using elementary equalities between various cables of the unknot and the Hopf link, we prove the Wheels and Wheeling conjectures of [5, 9], which give, respectively, the exact Kontsevich integral of the unknot and a map intertwining two natural products on a space of diagrams. It turns out that the Wheeling map is given by the Kontsevich integral of a cut Hopf link (a bead on a wire), and its i...
متن کامل1 4 A pr 2 00 4 A computation of Kontsevich Integral of torus knots ∗
We study the rational Kontsevich integral of torus knots. We construct explicitely a series of diagrams made of circles joined together in a tree-like fashion and colored by some special rational functions. We show that this series codes exactly the unwheeled rational Kontsevich integral of torus knots, and that it behaves very simply under branched coverings. Our proof is combinatorial. It use...
متن کاملA dissertation submitted in partial satisfaction of the requirements
Wheeling: A Diagrammatic Analogue of the Duflo Isomorphism We construct and prove a diagrammatic version of the Duflo isomorphism between the invariant subalgebra of the symmetric algebra of a Lie algebra and the center of the universal enveloping algebra. This version implies the original for metrized Lie algebras (Lie algebras with an invariant non-degenerate bilinear form). As an application...
متن کامل