Abstract
Using the method of continuous projective resolutions established by Alain Connes, we calculate the continuous Hochschild homology and cohomology groups of the Frechet algebra of smooth functions on a manifold M. These (co)homology groups are allowed to take values in the Frechet space E of smooth sections of a vector bundle E over M and in the strong dual E*. Moreover, we show that in the cohomological case the differential and continuous Hochschild cohomologies are naturally isomorphic.
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