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Some results of Hamiltonian homeomorphism on aspherical closed surfaces
澳门新葡8455最新网站:2017年06月12日 13:59 点击数:

报告人:王俭

报告地点:澳门新葡8455最新网站403室

报告澳门新葡8455最新网站:2017年06月15日星期四10:00-11:00

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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 (i.e., closed oriented surfaces with genus more than 1). 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 and orientation preserving homeomorphism of the 2-sphere by applying Brouwer plane translation theorem. Furthermore, we can prove a general version of C^1-Zimmer's conjecture based on the C^0-Schwarz's theorem.

 

主讲人概况:

王俭,博士毕业于法国巴黎第十三大学,现为马克斯普朗克研究所与南开大学陈省身数学研究所联合博士后。主要从事动力系统、遍历理论和辛几何的研究。

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