The Kontsevich Integral of the Unknot
نویسنده
چکیده
We mix together the Kontsevich integral, chord diagrams, Chinese characters, the Reshetikhin-Turaev knot invariants, the Poincare-Birkhoff-Witt theorem, the HarishChandra isomorphism, the Duflo isomorphism, the Kirillov formula and some minor Fourieranalysis computations. This enables us to make an intelligent guess for an exact formula for the Kontsevich integral of the unknot, and to conjecture a formula (also conjectured independently by Deligne [De]) for the relation between the two natural products on Chinese characters.
منابع مشابه
Wheels , 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...
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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...
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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...
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