Abstract
The problem of calculating of the global invariants for the action of the group of contact diffeomorphisms on itself by conjugations. The integral invariant for this action is obtained. This invariant is the analog of the Calabi invariant for the groups of symplectomorphisms of the unit disk. We normalize Cartan form for a given contact diffeomorphism and then consider the volume form on our compact manifold. This volume form is constructed with the help of the normalized Cartan form. The volume of our manifold with respect to this form is our intergal invariant.
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