Loops of Lagrangian submanifolds and pseudoholomorphic discs
نویسندگان
چکیده
The main theorem of this paper asserts that the inclusion of the space of projective Lagrangian planes into the space of Lagrangian submanifolds of complex projective space induces an injective homomorphism of fundamental groups. We introduce three invariants of exact loops of Lagrangian submanifolds that are modelled on invariants introduced by Polterovich for loops of Hamiltonian symplectomorphisms. One of these is the minimal Hofer length in a given Hamiltonian isotopy class. We determine the exact values of these invariants for loops of projective Lagrangian planes. The proof uses the Gromov invariants of an associated symplectic fibration over the 2-disc with a Lagrangian subbundle over the boundary.
منابع مشابه
Pseudoholomorphic discs attached to CR - submanifolds of almost complex spaces
Let E be a generic real submanifold of an almost complex manifold. The geometry of Bishop discs attached to E is studied in terms of the Levi form of E. Résumé. Nous étudions la géométrie des disques de Bishop attachés à une sous-variété réelle générique d’une variété presque complexe. MSC: 32H02, 53C15.
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