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| Deforming PSL(n,R) Hitchin component and Goldman symplectic form |
| 2017-10-11
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CAS Key Laboratory of Theoretical Physics |
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Institute of Theoretical Physics |
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Chinese Academy of Sciences |
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Seminar |
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Title
题目 |
Deforming PSL(n,R) Hitchin component and Goldman symplectic form |
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Speaker
报告人 |
Dr. Zhe Sun (孙哲) |
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Affiliation
所在单位 |
YMSC Tsinghua |
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Date
日期 |
3:30pm, Wed., Oct. 11, 2017 (10月11日下午3点半) |
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Venue
地点 |
Room 322, ITP |
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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. |
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Contact person
所内联系人 |
Yang Gang(杨刚) |
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