African Diaspora Journal of Mathematics

On Symplectomorphisms of the Symplectization of a Compact Contact Manifold

Augustin Banyaga

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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 $\underline {\phi}$ 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.

Article information

Source
Afr. Diaspora J. Math. (N.S.), Volume 9, Number 2 (2009), 66-73.

Dates
First available in Project Euclid: 31 March 2010

Permanent link to this document
https://projecteuclid.org/euclid.adjm/1270067489

Mathematical Reviews number (MathSciNet)
MR2575302

Zentralblatt MATH identifier
1241.53020

Subjects
Primary: 53C12: Foliations (differential geometric aspects) [See also 57R30, 57R32]
Secondary: 63C15

Keywords
symplectization of a contact manifold locally conformal symplectic manifold Lee form Lichnerowicz cohomology exact non-exact local conformal symplectic structure the extended Lee homomorphism the locally conformal symplectic calabi homomorphism

Citation

Banyaga, Augustin. On Symplectomorphisms of the Symplectization of a Compact Contact Manifold. Afr. Diaspora J. Math. (N.S.) 9 (2009), no. 2, 66--73. https://projecteuclid.org/euclid.adjm/1270067489


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