TY  - THES
A1  - Schlierkamp, Thorben
T1  - De Rham and Cech-de Rham Cohomologies of Smooth Foliated Manifolds
N2  - 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.
T3  - ohne Schriftenreihe - 0 
KW  - de Rham cohomology
KW  - foliated manifolds
KW  - Cech-de Rham cohomology
KW  - Cech cohomology of leafwise constant functions
KW  - Differentialgeometrie
Y1  - 2021
UR  - https://ubt.opus.hbz-nrw.de/frontdoor/index/index/docId/1635
UR  - https://nbn-resolving.org/urn:nbn:de:hbz:385-1-16353
PB  - -
CY  - -
ER  -