https://ubt.opus.hbz-nrw.deOPUS documents
https://ubt.opus.hbz-nrw.de/index/index/
Mon, 08 Mar 2021 09:45:11 +0200Mon, 08 Mar 2021 09:45:11 +0200De Rham and Cech-de Rham Cohomologies of Smooth Foliated Manifolds
https://ubt.opus.hbz-nrw.de/frontdoor/index/index/docId/1635
In order to classify smooth foliated manifolds, which are smooth maifolds equipped with a smooth foliation, we introduce the de Rham cohomologies of smooth foliated manifolds. These cohomologies are build in a similar way as the de Rham cohomologies of smooth manifolds. We develop some tools to compute these cohomologies. For example we proof a Mayer Vietoris theorem for foliated de Rham cohomology and show that these cohomologys are invariant under integrable homotopy. A generalization of a known Künneth formula, which relates the cohomologies of a product foliation with its factors, is discussed. In particular, this envolves a splitting theory of sequences between Frechet spaces and a theory of projective spectrums. We also prove, that the foliated de Rham cohomology is isomorphic to the Cech-de Rham cohomology and the Cech cohomology of leafwise constant functions of an underlying so called good cover.Thorben Schlierkampdoctoralthesishttps://ubt.opus.hbz-nrw.de/frontdoor/index/index/docId/1635Tue, 03 Aug 2021 09:45:11 +0200