Quantization of linear Poisson structures and degrees of maps

Details Quantization of linear Poisson structures and degrees of maps Quantization of linear Poisson structures and degrees of maps

2002-10-07

arxiv.org/abs/math/0210107v3

Mathematics

Geometric Topology

An extended and modified version; 18 pages, 10 figures. To appear in Let. Math. Phys

Scientific paper

10.1023/B:MATH.0000017675.20434.

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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