Moscow--Petersburg seminar on low-dimensional mathematics
SPb, PDMI, 13.12.2002, 16:00--17:45, room 311

"Kontsevich's integral and identities for infinite series."
S.Duzhin (PDMI)

The Kontsevich integral of a Morse knot in 3-space
is a far-going generalization of the Gauss integral formula
for two space curves. Both integrals provide topological
invariants of spacial curves (knots and 2-components links, respectively).
Gauss's integral is equal to the linking number --- an integer, which
is not evident apriori.
Kontsevich's integral, upon proper normalization, gives the universal 
finite type invariant; it is represented as an infinite sum of
chord diagrams with rational coefficients. Computing the Kontsevich 
integral even for simple knots and tangles, one arrives at unexpected
identities between different sums of polylogarithmic type.

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Seminar home-page http://www.pdmi.ras.ru/~lowdimma