ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

6. Topology

1991 MS Classification: 55, 57, 58 Rudyak, Yuli B., Universität–GH Siegen, Germany Lusternik–Schnirelmann category of symplectic manifolds and the Arnold conjecture The Arnold conjecture (see the reference) claims that, for every Hamiltonian symplectomorphism ϕ : M → M of a closed symplectic manifold (M, ω), the number of fixed points of ϕ is at least the minimal number of critical points of a smooth function on M. Here we prove this conjecture for every manifold (M, ω) with ω|_{π_{2}(M)} = 0 = c_{1}|_{π_{2}(M)}. This is the joint result with J. Oprea. Reference: V. I. Arnold, Mathematical Methods in Classical Mechanics. Springer, Berlin Heidelberg New York 1989.