Morse theory for fixed points of symplectic diffeomorphisms. (English) Zbl 0617.53042

The author announces the following result: If P is a compact closed symplectic manifold with \(\pi_ 2(P)=0\) and \(\phi\) : \(P\to P\) is an exact diffeomorphism all of whose fixed points are nondegenerate, then the number of fixed points of \(\phi\) is greater than or equal to the sum of the Betti numbers of P with respect to \(Z_ 2\)-coefficients. This extends a result by M. Gromov [Invent. Math. 82, 307-347 (1985; Zbl 0592.53025)].
Reviewer: J.Weinstein


53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
57R50 Differential topological aspects of diffeomorphisms
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems


Zbl 0592.53025
Full Text: DOI


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