The Künneth formula for nuclear $DF$-spaces and Hochschild cohomology
| dc.creator | Lykova, Zinaida A. | |
| dc.date | 2007-09-12 | |
| dc.date.accessioned | 2026-07-07T08:29:11Z | |
| dc.date.available | 2026-07-07T08:29:11Z | |
| dc.description | We consider complexes $(\X, d)$ of nuclear Fréchet spaces and continuous boundary maps $d_n$ with closed ranges and prove that, up to topological isomorphism, $ (H_{n}(\X, d))^*$ $\iso$ $H^{n}(\X^*,d^*),$ where $(H_{n}(\X,d))^*$ is the strong dual space of the homology group of $(\X,d)$ and $ H^{n}(\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 $\hat{\otimes}$-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 $\hat{\otimes}$-algebras which are Fréchet spaces or nuclear $DF$-spaces. | |
| dc.description | 31 pages | |
| dc.identifier | https://arxiv.org/abs/0709.1911 | |
| dc.identifier | http://arxiv.org/abs/0709.1911 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/137876 | |
| dc.subject | K-Theory and Homology | |
| dc.subject | Functional Analysis | |
| dc.subject | 19D55 (Primary) 46H40, 55U25 (Secondary) | |
| dc.title | The Künneth formula for nuclear $DF$-spaces and Hochschild cohomology | |
| dc.type | text |