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 -