Lusternik-Schnirelman-theory for Lagrangian intersections

  • H. Hofer

    Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903

Abstract

Consider a compact symplectic manifold (M, ω) together with a pair (L, L1) of isotopic compact Lagrangian submanifolds such that π2(M, L) = 0.

Using Gromov’s theory of (almost) holomorphic curves the cohomological properties of a family of holomorphic disks are studied. By means of a stretching construction for those disks and a Lusternik-Schnirelman-Theory in compact topological spaces cuplength estimates for the intersection set L ∩ L1 are derived.

Résumé

On examiṅe une variété symplectique compacte (M, ω) munie d’un couple (L0, L1) de sous-variétés lagrangiennes isotopes telles que π2(M, L) = 0.

En utilisant la théorie des courbes presque holomorphes, développée par Gromov, on étudie la cohomologie de certaines familles de disques holomorphes. On en déduit, par la théorie de Lusternik-Schnirelman, des estimations du cuplength de l’intersection L0 ∩ L1.

Cite this article

H. Hofer, Lusternik-Schnirelman-theory for Lagrangian intersections. Ann. Inst. H. Poincaré Anal. Non Linéaire 5 (1988), no. 5, pp. 465–499

DOI 10.1016/S0294-1449(16)30339-0