Formule d'homotopie entre les complexes de Hochschild et de De Rham |
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Authors: | Gilles Halbout |
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Institution: | (1) Institut de Recherche Mathématique Avancée, Université Louis Pasteur – CNRS, 7, rue René Descartes, 67084 Strasbourg Cedex, France |
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Abstract: | Let k be the field or let M be the space k
n and let A be the algebra of polynomials over M. We know from Hochschild and co-workers that the Hochschild homology H
·(A,A) is isomorphic to the de Rham differential forms over M: this means that the complexes (C
·(A,A),b) and (·(M), 0) are quasi-isomorphic. In this work, I produce a general explicit homotopy formula between those two complexes. This formula can be generalized when M is an open set in a complex manifold and A is the space of holomorphic functions over M. Then, by taking the dual maps, I find a new homotopy formula for the Hochschild cohomology of the algebra of smooth fonctions over M (when M is either a complex or a real manifold) different from the one given by De Wilde and Lecompte. I will finally show how this formula can be used to construct an homotopy for the cyclic homology. |
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