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.
Publié le : 2009-09-15
Classification:
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,
53C12,
63C15
@article{1270067489,
author = {Banyaga, Augustin},
title = {On Symplectomorphisms of the Symplectization of a Compact
Contact Manifold},
journal = {Afr. Diaspora J. Math. (N.S.)},
volume = {9},
number = {2},
year = {2009},
pages = { 66-73},
language = {en},
url = {http://dml.mathdoc.fr/item/1270067489}
}
Banyaga, Augustin. On Symplectomorphisms of the Symplectization of a Compact
Contact Manifold. Afr. Diaspora J. Math. (N.S.), Tome 9 (2009) no. 2, pp. 66-73. http://gdmltest.u-ga.fr/item/1270067489/