Quantization of linear Poisson structures and degrees of maps

Michael Polyak

doi:10.1023/b:math.0000017675.20434.79

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Quantization of linear Poisson structures and degrees of maps

Michael Polyak

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Abstract

Kontsevich's formula for a deformation quantization of Poisson structures involves a Feynman series of graphs, with the weights given by some complicated integrals (using certain pullbacks of the standard angle form on a circe). We explain the geometric meaning of this series as degrees of maps of some grand configuration spaces; the associativity proof is also interpreted in purely homological terms. An interpretation in terms of degrees of maps shows that any other 1-form on the circle also leads to a *-product and allows one to compare these products.

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Michael Polyak. 2003-09-04. Quantization of linear Poisson structures and degrees of maps. https://doi.org/10.1023/b:math.0000017675.20434.79

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