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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

##### MSC:
 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
##### Keywords:
symplectic manifold; exact diffeomorphism; fixed points
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##### References:
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