Universität zu Köln

Niederkrüger, Klaus (2005). Compact Lie group actions on contact manifolds. PhD thesis, Universität zu Köln.

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Abstract

The main result in this thesis is the classification of SO(3)-actions on contact 5-manifolds. Using properties of the moment map, one can reduce the manifold to a 3-dimensional contact manifold with an S^1-action. This works everywhere outside of the singular orbits. For the singular orbits three models can be given that describe all possible cases. The 5-manifold is then obtained by gluing the singular set onto the 3-dimensional S^1-manifold in a compatible way. As it is well-known, S^1-bundles over a closed surface are classified by an integer called the Euler number. A similar invariant can be recovered in our 3-dimensional setting. We call it the Dehn-Euler number.