On symplectic manifolds with aspherical symplectic form

Details On symplectic manifolds with aspherical symplectic form On symplectic manifolds with aspherical symplectic form

1999-07-31

arxiv.org/abs/math/9908001v1

Mathematics

Differential Geometry

12 pages, amstex

Scientific paper

We consider closed symplectically aspherical manifolds, i.e. closed symplectic manifolds $(M,\omega)$ satisfying the condition $[\omega]|_{\pi_2M}=0$. Rudyak and Oprea [RO] remarked that such manifolds have nice and controllable homotopy properties. Now it is clear that these properties are mostly determined by the fact that the strict category weight of $[\omega]$ equals 2. We apply the theory of strict category weight to the problem of estimating the number of closed orbits of charged particles in symplectic magnetic fields. In case of symplectically aspherical manifolds our theory enables us to improve some known estimations.

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