Wheels, wheeling, and the Kontsevich integral of the Unknot | Zendy

Dror Bar-Natan | Zendy; Stavros Garoufalidis | Zendy; Lev Rozansky | Zendy; Dylan P. Thurston | Zendy

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Wheels, wheeling, and the Kontsevich integral of the Unknot

Author(s) -

Dror Bar-Natan,

Stavros Garoufalidis,

Lev Rozansky,

Dylan P. Thurston

Publication year - 2000

Publication title -

israel journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.168

H-Index - 63

eISSN - 1565-8511

pISSN - 0021-2172

DOI - 10.1007/bf02810669

Subject(s) - unknot , mathematics , conjecture , pure mathematics , mathematical proof , lie algebra , algebra over a field , space (punctuation) , transcendental number , knot (papermaking) , mathematical analysis , geometry , linguistics , philosophy , chemical engineering , engineering

We conjecture an exact formula for the Kontsevich integral of the unknot, andalso conjecture a formula (also conjectured independently by Deligne) for therelation between the two natural products on the space of Chinese characters.The two formulas use the related notions of "Wheels" and "Wheeling". We provethese formulas "on the level of Lie algebras" using standard techniques fromthe theory of Vassiliev invariants and the theory of Lie algebras.

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