Contact homology of toroidal manifolds. (Homologie de contact des variétés toroïdales.)
Controlled constructions of Reeb fields and applications. (Constructions contrôlées de champs de Reeb et applications.)
Correction to “Properties of pseudoholomorphic curves in symplectisations. I : asymptotics”
Diffeomorphisms, symplectic forms and Kodaira fibrations.
Finitude homotopique et isotopique des structures de contact tendues
Soit V une variété close de dimension 3. Dans cet article, on montre que les classes dhomotopie de champs de plans sur V qui contiennent des structures de contact tendues sont en nombre fini et que, si V est atoroïdale, les classes disotopie des structures de contact tendues sur V sont elles aussi en nombre fini.
First steps in stable Hamiltonian topology
In this paper we study topological properties of stable Hamiltonian structures. In particular, we prove the following results in dimension three: The space of stable Hamiltonian structures modulo homotopy is discrete; stable Hamiltonian structures are generically Morse-Bott (i.e. all closed orbits are Bott nondegenerate) but not Morse; the standard contact structure on is homotopic to a stable Hamiltonian structure which cannot be embedded in . Moreover, we derive a structure theorem for stable...
Foliations and contact structures.
Formality and the Lefschetz property in symplectic and cosymplectic geometry
We review topological properties of Kähler and symplectic manifolds, and of their odd-dimensional counterparts, coKähler and cosymplectic manifolds. We focus on formality, Lefschetz property and parity of Betti numbers, also distinguishing the simply-connected case (in the Kähler/symplectic situation) and the b1 = 1 case (in the coKähler/cosymplectic situation).
Formes de contact ayant le même champ de Reeb
2000 Mathematics Subject Classification: 37J55, 53D10, 53D17, 53D35.In this paper, we study contact forms on a 3-manifold having a common Reeb vector field R. The main result is that when the contact forms induce the same orientation, they are diffeomorphic.
Generating function polynomials for Legendrian links.
Handle attaching in symplectic homology and the Chord Conjecture
Arnold conjectured that every Legendrian knot in the standard contact structure on the 3-sphere possesses a haracteristic chord with respect to any contact form. I confirm this conjecture if the know has Thurston-Bennequin invariant . More generally, existence of chords is proved for a standard Legendrian unknot on the boundary of a subcritical Stein manifold of any dimension. There is also a multiplicity result which implies in some situations existence of infinitely many chords. The proof relies...
Homotopy properties of Hamiltonian group actions.
Knot and braid invariants from contact homology. I.
Knot and braid invariants from contact homology. II.
Length minimizing Hamiltonian paths for symplectically aspherical manifolds
In this note we consider the length minimizing properties of Hamiltonian paths generated by quasi-autonomous Hamiltonians on symplectically aspherical manifolds. Motivated by the work of Polterovich and Schwarz, we study the role, in the Floer complex of the generating Hamiltonian, of the global extrema which remain fixed as the time varies. Our main result determines a natural condition which implies that the corresponding path minimizes the positive Hofer length. We use this to prove that a quasi-autonomous Hamiltonian...
Levi-flat filling of real two-spheres in symplectic manifolds (I)
Let be a manifold with an almost complex structure tamed by a symplectic form . We suppose that has the complex dimension two, is Levi-convex and with bounded geometry. We prove that a real two-sphere with two elliptic points, embedded into the boundary of can be foliated by the boundaries of pseudoholomorphic discs.
Levi-flat filling of real two-spheres in symplectic manifolds (II)
We consider a compact almost complex manifold with smooth Levi convex boundary and a symplectic tame form . Suppose that is a real two-sphere, containing complex elliptic and hyperbolic points and generically embedded into . We prove a result on filling by holomorphic discs.
New examples of compact cosymplectic solvmanifolds
In this paper we present new examples of -dimensional compact cosymplectic manifolds which are not topologically equivalent to the canonical examples, i.e., to the product of the -dimensional real torus and the -dimensional complex projective space, with and These new examples are compact solvmanifolds and they are constructed as suspensions with fibre the -dimensional real torus. In the particular case using the examples obtained, we conclude that a -dimensional compact flat orientable...
On Arnold's conjecture for symplectic fixed points
On nonformal simply-connected symplectic manifolds.