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De Rham and Cech-de Rham Cohomologies of Smooth Foliated Manifolds
- 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.
Verfasserangaben: | Thorben Schlierkamp |
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URN: | urn:nbn:de:hbz:385-1-16353 |
DOI: | https://doi.org/10.25353/ubtr-xxxx-68fa-85dc |
Schriftenreihe (Bandnummer): | ohne Schriftenreihe (0) |
Verlag: | - |
Verlagsort: | - |
Gutachter: | Jochen Wengenroth, Leonhard Frerick |
Betreuer: | Jochen Wengenroth |
Dokumentart: | Dissertation |
Sprache: | Englisch |
Datum der Fertigstellung: | 16.07.2021 |
Datum der Veröffentlichung: | 03.08.2021 |
Veröffentlichende Institution: | Universität Trier |
Titel verleihende Institution: | Universität Trier, Fachbereich 4 |
Datum der Abschlussprüfung: | 10.05.2021 |
Datum der Freischaltung: | 03.08.2021 |
Freies Schlagwort / Tag: | Cech cohomology of leafwise constant functions; Cech-de Rham cohomology; de Rham cohomology; foliated manifolds |
GND-Schlagwort: | Differentialgeometrie |
Seitenzahl: | 116 |
Institute: | Fachbereich 4 |
DDC-Klassifikation: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Lizenz (Deutsch): | CC BY-NC: Creative-Commons-Lizenz 4.0 International |