5-dimensional contact SO(3)-manifolds and Dehn twists
Abstract
Description
In this paper the 5-dimensional contact SO(3)-manifolds are classified up to equivariant 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-manifoldswith 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.
16 pages, 1 figure; simplification of arguments by restricting classification to coorientation preserving contactomorphisms
16 pages, 1 figure; simplification of arguments by restricting classification to coorientation preserving contactomorphisms