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 circle). 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 star-product and allows one to compare these products.
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Polyak, M. Quantization of Linear Poisson Structures and Degrees of Maps. Letters in Mathematical Physics 66, 15–35 (2003). https://doi.org/10.1023/B:MATH.0000017675.20434.79
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DOI: https://doi.org/10.1023/B:MATH.0000017675.20434.79