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On Symplectomorphisms of the Symplectization of a Compact Contact Manifold

Volume 9, Number 2 (2010), 66 - 73

On Symplectomorphisms of the Symplectization of a Compact Contact Manifold

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Abstract

Let $(N,\alpha)$ be a compact contact manifold and $(N \times {\mathbb R}, d(e^t\alpha))$ its symplectization. We show that the group $G$ which is the identity component in the group of symplectic diffeomorphisms $\phi$ of $(N \times {\mathbb R}, d(e^t\alpha))$ that cover diffeomorphisms $\phi$− of $N\times S^1$ is simple, by showing that $G$ is isomorphic to the kernel of the Calabi homomorphism of the associated locally conformal symplectic structure.