Colloquium

Colloquium
The Arnold conjecture and Floer theory Yoshiro YABU 6月2日(金) 13時30分 In the 1960s, Arnold conjectured that for a generic Hamiltonian system on a symplectic manifold $M$, the number of periodic orbits is greater than the sum of the Betti numbers of $M$. Floer [1] proved this conjecture under the assumption that a symplectic manifold is monotone. His proof is based on an infinite-dimensional version of Morse theory with an application of pseudo-holomorphic curves introduced by Gromov [2]. In this talk, Floer's approach and an extension will be outlined. References: [1] A. Floer, Commun. Math. Phys. {\bf 120}, 575-611 (1989). [2] M. Gromov, Invent. Math. {\bf 82}, 307-347 (1985).

The Arnold conjecture and Floer theory

Yoshiro YABU

6月2日(金) 13時30分

In the 1960s, Arnold conjectured that for a generic Hamiltonian system on a symplectic manifold $M$, the number of periodic orbits is greater than the sum of the Betti numbers of $M$. Floer [1] proved this conjecture under the assumption that a symplectic manifold is monotone. His proof is based on an infinite-dimensional version of Morse theory with an application of pseudo-holomorphic curves introduced by Gromov [2].

In this talk, Floer's approach and an extension will be outlined.

References:
[1] A. Floer, Commun. Math. Phys. {\bf 120}, 575-611 (1989).
[2] M. Gromov, Invent. Math. {\bf 82}, 307-347 (1985).