Complete integrable system on the Hitchin component

发布时间:2017-08-19浏览次数:936

Speaker:Zhe SUN

Institution: Tsinghua University

Title: Complete integrable system on the Hitchin component 

Time:2017.08.19, 16:55-17:45

Location:Room 503, Gewu Building 

Abstract: This is joint work with Anna Wienhard and Tengren Zhang. ) Let S be a closed, connected, oriented surface of genus at least 2. It is well-known that on Teichmuller space, the twist flows along a pants decomposition of S is a maximal family of Poisson commuting Hamiltonian flows. We prove that any ideal triangulation on S determines a symplectic trivialization (with respect to the Goldman symplectic form) of the tangent bundle of the PSL(n,R) Hitchin component. One can then consider the parallel flows with respect to the flat structure given by this trivialization. We give a geometric description of all such flows in terms of explicit deformations of the associated Frenet curves, and prove that all such flows are Hamiltonian. Applying this to a particular ideal triangulation allows us compute the Goldman symplectic pairing explicitly. As a consequence, we find a maximal family of Poisson commuting Hamiltonian flows on the PSL(n,R) Hitchin component and a global Darboux coordinates for PSL(n,R) Hitchin component.


Copyright (C)2023 哈尔滨工业大学数学研究院版权所有
人才招聘:
联系我们:
电话:86413107      邮箱:IASM@hit.edu.cn
地址:哈尔滨市南岗区西大直街92号
技术支持:哈尔滨工业大学网络安全和信息化办公室