On symplectic manifolds with aspherical symplectic form

Yuli B. Rudyak, Aleksy Tralle

DOI: http://dx.doi.org/10.12775/TMNA.1999.038

Abstract


We consider closed symplectically aspherical manifolds, i.e. closed
symplectic manifolds $(M,\omega)$ satisfying the condition
$[\omega]|_{\pi_2M}=0$. Rudyak and Opre[< i> On the Lustrnik–Schnirelmann category of symplectic
manifolds and the Arnold conjecture< /i> , Math. Z.
< b> 230< /b> (1999), 673–678] 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.

Keywords


Lusternik-Schnirelmann category; sympletic manifolds

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