Five-Dimensional Contact SU(2)- and SO(3)-Manifolds and Dehn Twists

In the first part of this paper the five-dimensional contact SO(3)-manifolds are classified up to equivariant coorientation preserving contactomorphisms. The construction of such manifolds with singular orbits requires the use of generalized Dehn twists. We show as an application that all simply connected 5-manifolds with singular orbits are realized by a Brieskorn manifold with exponents (k,2,2,2). The standard contact structure on such a manifold gives right-handed Dehn twists, and a second contact structure defined in the article gives left-handed twists. In an appendix we also describe the classification of five-dimensional contact SU(2)-manifolds.