トポロジー火曜セミナー

過去の記録 ~07/13次回の予定今後の予定 07/14~

開催情報 火曜日 17:00~18:30 数理科学研究科棟(駒場) 056号室
担当者 河澄 響矢, 北山 貴裕, 逆井卓也
セミナーURL http://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index.html

2017年01月24日(火)

17:00-18:00   数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00
折田 龍馬 氏 (東京大学大学院数理科学研究科)
閉シンプレクティック多様体上のハミルトン力学系における無限個の非可縮周期軌道の存在について (JAPANESE)
[ 講演概要 ]
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.