  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.
