Polygonal combinatorics for algebraic cycles

Herbert Gangl (Durham)

Wednesday 1st October, 2008 16:00-17:00 214


Starting from comparably explicit objects (algebraic cycles), Bloch and Kriz have given a tentative definition of a small yet rich category of motives (mixed Tate motives), at least over a field. They also exhibited a distinguished class of cycles corresponding to polylogarithms. One can also find _multiple_ polylogarithms as algebraic cycles, and it turns out that their differential structure can be conveniently described with the help of combinatorics of polygons. This leads to a coproduct on polygons which is a variant of the Connes-Kreimer coproduct on rooted trees.

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