Wheels, wheeling, and the Kontsevich integral of the Unknot |
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| Authors: | Dror Bar-Natan Stavros Garoufalidis Lev Rozansky Dylan P. Thurston |
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| Affiliation: | (1) Institute of Mathematics, The Hebrew University of Jerusalem Giv'at-Ram, 91904 Jerusalem, Israel;(2) Department of Mathematics, Harvard University, 02138 Cambridge, MA, USA;(3) Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 60607-7045 Chicago, IL, USA;(4) Department of Mathematics, University of California at Berkeley, 94720-3840 Berkeley, CA, USA;(5) Present address: School of Mathematics, Georgia Institute of Technology, 30332-0160 Atlanta, GA, USA;(6) Present address: Department of Mathematics, Yale University, 10 Hillhouse Avenue, P.O. Box 208283, 06520-8283 New Haven, CT, USA |
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| Abstract: | 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 “Wheeing”. 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. In a brief epilogue we report on recent proofs of our full conjectures, by Kontsevich [Ko2] and by DBN, DPT, and T. Q. T. Le, [BLT]. This paper is available electronically |
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