报告题目：

Some results of Hamiltonian homeomorphism on aspherical closed surfaces

报 告 人：

王俭 博士后（南开大学陈省身数学研究所）

报告时间：

2017年12月19日 9:50--10:50

报告地点：

数学院东北楼四楼报告厅（404）

报告摘要：

On closed symplectically aspherical manifolds, Schwarz proved a classical result that the action function of a nontrivial Hamiltonian diffeomorphism is not constant by using Floer homology. In this talk, we generalize Schwarz's theorem to the $C^0$-case on closed aspherical surfaces. Our methods involve the theory of transverse foliations for dynamical systems of surfaces inspired by Le Calvez and its recent progresses. As an application, we prove that the contractible fixed points set (and consequently the fixed points set) of a nontrivial Hamiltonian homeomorphism is not connected. We also get a similar result of an area preserving and orientation preserving homeomorphism of the two sphere by applying Brouwer plane translation theorem. In the end, we will give further applications that we obtained recently based on the $C^0$-Schwarz theorem.