Аннотация:
After a brief review of the Arnold's Conjecture, I will give an overview
of the proof of the following joint result with Blumberg: for every
closed symplectic manifold, the number of time-$1$ periodic orbits of a
non-degenerate Hamiltonian is bounded below by the rank of the
cohomology with coefficients in any field. The case of characteristic
$0$ was proved by Fukaya and Ono as well as Li and Tian. The new
ingredient in our proof is the construction of generalized Floer
cohomology groups with coefficients in Morava $K$-theory. This means
that we have to use higher dimensional moduli spaces of
pseudo-holomorphic curves, and extract “fundamental chains” in
generalized homology.
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