Quantization of linear Poisson structures and degrees of maps
Geometric Topology
2009-11-07 v3 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.math/0210107,
title = {Quantization of linear Poisson structures and degrees of maps},
author = {Michael Polyak},
journal= {arXiv preprint arXiv:math/0210107},
year = {2009}
}
Comments
An extended and modified version; 18 pages, 10 figures. To appear in Let. Math. Phys