
Deforming PSL(n,R) Hitchin component and Goldman symplectic form 
20171011
Text Size:
A A A 
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 wellknown 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) 



