Lusternik-Schnirelman-theory for Lagrangian intersections (Q1118874)

The abstract framework used in this paper consists in a compact symplectic manifold (M,\(\omega)\) together with a pair \((L,L_ 1)\) of isotopic submanifolds such that \(\pi_ 2(M,L)=0\). Using \textit{M. Gromov}'s theory of (almost) holomorphic curves [Invent. Math. 82, 307- 347 (1985; Zbl 0592.53025)] the cohomological properties of a family of holomorphic disks are studied. Making use of a Ljusternik-Schnirelman theory in compact topological spaces cuplength estimates for the intersection set \(L\cap L_ 1\) are derived.