5-dimensional contact SO(3)-manifolds and Dehn twists

Details 5-dimensional contact SO(3)-manifolds and Dehn twists 5-dimensional contact SO(3)-manifolds and Dehn twists

2004-09-06

arxiv.org/abs/math/0409082v2

Geom. Dedicata 117 (2006), 85-110. (Five-Dimensional Contact SU(2)- and SO(3)-Manifolds and Dehn Twists)

Mathematics

Symplectic Geometry

16 pages, 1 figure; simplification of arguments by restricting classification to coorientation preserving contactomorphisms

Scientific paper

10.1007/s10711-005-9014-3

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.

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