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Sfb 288 Differential Geometry and Quantum Physics |
Abstract for Sfb Preprint No. 299
On continuous Hochschild homology and cohomology groups M. Pflaum
Using the method of continuous projective resolutions established by Alain Connes we calculate the continuous Hochschild homology and cohomology groups of the Fréchet algebra of smooth functions on a manifold $M$. These (co)homology groups are allowed to take values in the Fréchet space $cE$ of smooth sections of a vector bundle $E$ over $M$ and in the strong dual $cE^*$. Moreover we show that in the cohomological case the differential and continuous Hochschild cohomologies are naturally isomorphic.
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