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Cuplength estimates on Lagrangian intersections. (English) Zbl 0683.58017
This article presents a proof of the following version of Arnold’s conjecture: “Let L be a compact Lagrangian submanifold of a symplectic manifold P, such that \(\pi_ 2(P,L)=0\). Then for any exact diffeomorphism \(\phi\), the number of intersections of \(\phi\) (L) with L is greater than or equal to the \(Z_ 2\)-cuplength of L.” This theorem implies the following corollary: “If P is a compact symplectic manifold with \(\pi_ 2(P)=0\), then the number of fixed points of any exact diffeomorphism of P is greater than or equal to the \(Z_ 2\)-cuplength of P.”
Reviewer: V.Perlick

37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
Full Text: DOI
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