The Künneth Formula for Nuclear Df -spaces and Hochschild Cohomology
نویسندگان
چکیده
We consider complexes (X , d) of nuclear Fréchet spaces and continuous boundary maps dn with closed ranges and prove that, up to topological isomorphism, (Hn(X , d)) ∗ ∼= H(X ∗, d∗), where (Hn(X , d)) ∗ is the strong dual space of the homology group of (X , d) and H(X ∗, d∗) is the cohomology group of the strong dual complex (X ∗, d∗). We use this result to establish the existence of topological isomorphisms in the Künneth formula for the cohomology of complete nuclear DF -complexes and in the Künneth formula for continuous Hochschild cohomology of nuclear ⊗̂-algebras which are Fréchet spaces or DF -spaces for which all boundary maps of the standard homology complexes have closed ranges. We describe explicitly continuous Hochschild and cyclic cohomology groups of certain tensor products of ⊗̂-algebras which are Fréchet spaces or nuclear DF -spaces. 2000 Mathematics Subject Classification: Primary 19D55, 22E41, 46H40, 55U25.
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