The thesis deals with contact manifolds and their groups of transformations and relatedly with contact fibre bundles. We apply the framework of convenient calculus on in finite dimensional smooth manifolds to study the Chern-Weil theory of groups of strict contactomorphisms producing several non-vanishing type results on the cohomology of the classifying spaces of these groups. Moreover, we prove that the space of isocontact embeddings of one contact manifold to another can be given the structure of a smooth manifold and a principal bundle. Using this we describe a particular smooth model of the classifying space for the group Cont+(M; ) of (co-orientation preserving) contactomorphisms of a closed contact manifold (M; ). Lastly, we show that the standard action of the unitary group U(2) on the standard contact 3-sphere S3 induces a homotopy equivalence Cont+(S3; std) ' U(2).
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:619183 |
| Date | January 2014 |
| Creators | Spáčil, Oldřich |
| Publisher | University of Aberdeen |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=211433 |
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