Commutators of contactomorphisms

Details Commutators of contactomorphisms Commutators of contactomorphisms

2008-03-30

arxiv.org/abs/0803.4338v5

Advances in Math. 225(2010), 3291-3326

Mathematics

Differential Geometry

revised version; 38 pages

Scientific paper

The group of volume preserving diffeomorphisms, the group of symplectomorphisms and the group of contactomorphisms constitute the classical groups of diffeomorphisms. The first homology groups of the compactly supported identity components of the first two groups have been computed by Thurston and Banyaga, respectively. In this paper we solve the long standing problem on the algebraic structure of the third classical diffeomorphism group, i.e. the contactomorphism group. Namely we show that the compactly supported identity component of the group of contactomorphisms is perfect and simple (if the underlying manifold is connected). The result could be applied in various ways.

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