Sur les transformations de contact au-dessus des surfaces

Giroux, Emmanuel

HAL, ISBN: 2-940264-05-8 / Harvested from HAL

Résumé

Let S be a compact surface - or the interior of a compact surface - and let V be the manifold of cooriented contact elements of S equiped with its canonical contact structure. A diffeomorphism of V that preserves the contact structure and its coorientation is called a contact transformation over S. We prove the following results. 1) If S is neither a sphere nor a torus then the inclusion of the diffeomorphism group of S into the contact transformation group is 0-connected. 2) If S is a sphere then the contact transformation group is connected. 3) if S is a torus then the homomorphism from the contact transformation group of S to the automorphism group of $H_1(V) \\simeq Z^3$ has connected fibers and the image is (known to be) the stabilizer of $Z^2 \\times \\{0\\}$).

Détail

Publié le : 2001-07-05
Classification:  [MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT],  [MATH.MATH-SG]Mathematics [math]/Symplectic Geometry [math.SG],  [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG]