Tuesday Seminar on Topology

Seminar information archive ~03/28Next seminarFuture seminars 03/29~

Date, time & place Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.)
Organizer(s) KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya

2017/01/24

17:00-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Ryuma Orita (The University of Tokyo)
On the existence of infinitely many non-contractible periodic trajectories in Hamiltonian dynamics on closed symplectic manifolds (JAPANESE)
[ Abstract ]
We show that the presence of a non-contractible Hamiltonian one-periodic trajectory in a closed symplectic manifold yields the existence of infinitely many non-contractible periodic trajectories, provided that the symplectic form is aspherical and the fundamental group is virtually abelian. Moreover, we also show that a similar statement holds for closed monotone or negative monotone symplectic manifolds having virtually abelian fundamental groups. These results are certain generalizations of works by Ginzburg and Gurel who proved a similar statement holds for atoroidal or toroidally monotone closed symplectic manifolds. The proof is based on the machinery of filtered Floer--Novikov homology for non-contractible periodic trajectories.