The Hochschild cohomology of a closed manifold |
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Authors: | Yves Felix, Jean-Claude Thomas Micheline Vigué -Poirrier |
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Affiliation: | (1) Département de mathématique, Université Catholique de Louvain, 2, Chemin du Cyclotron, 1348 Louvain la Neuve, Belgium;(2) Département de mathématique, Université dAngers, 2, Boulevard Lavoisier, 49045 Angers, France;(3) Institut Galilée, Université de Paris-Nord, 93430 Villetaneuse, France |
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Abstract: | Let M be a closed orientable manifold of dimension d and be the usual cochain algebra on M with coefficients in a field k. The Hochschild cohomology of M, is a graded commutative and associative algebra. The augmentation map induces a morphism of algebras . In this paper we produce a chain model for the morphism I. We show that the kernel of I is a nilpotent ideal and that the image of I is contained in the center of , which is in general quite small. The algebra is expected to be isomorphic to the loop homology constructed by Chas and Sullivan. Thus our results would be translated in terms of string homology. |
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