Abstract
Let k be the first C and R let M be the space k n and let A be the algebra of polynomials over M. We produce a general explicit homotopy formula between the complex of Hochschild chains of A, ( C •( A), b) and the de Rham complex of M, (Ω •( M), 0). This formula can be generalized when M is a contractible open set in a complex manifold and A is the space of holomorphic functions over M. Then we find a new homotopy formula for the Hochschild cohomology of the algebra of smooth fonctions over M different from the one given in [5]. Finally, we show how this formula can be used to construct a homotopy for the cyclic homology.
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