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Deforming PSL(n,R) Hitchin component and Goldman symplectic form
2017-10-11  【 】【打印】【关闭

CAS Key Laboratory of Theoretical Physics

Institute of Theoretical Physics

 Chinese Academy of Sciences

Seminar

Title

题目

Deforming PSL(n,R) Hitchin component and Goldman symplectic form

Speaker

报告人

Dr. Zhe Sun (孙哲)

Affiliation

所在单位

YMSC Tsinghua

Date

日期

3:30pm, Wed., Oct. 11, 2017 (10月11日下午3点半)

Venue

地点

Room 322, ITP

Abstract

摘要

(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 length functions along a pants decomposition of S is a maximal family of Poisson commuting Hamiltonian functions. We prove that any ideal triangulation and any bridge system on S determine 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, thus we can compute the Hamiltonian functions of these Hamiltonian flows explicitly. As a consequence, we find a maximal family of Poisson commuting Hamiltonian functions on the PSL(n,R) Hitchin component and a global Darboux coordinates on PSL(n,R) Hitchin component.

Contact person

所内联系人

Yang Gang(杨刚)
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