Hitchin分支中长度函数的泊松括号
The Poisson Bracket of Length functions in the Hitchin Component
摘要：
泰希米勒空间上的沃尔伯特余弦公式给出了闭曲线$α,β$的测地线长度函数$l_α,l_β$的Weil-Petersson泊松括号$\{l_α, l_β\}$，作为相关测地线相交角的余弦之和。这是最近推广到希钦表示的拉布里。在本文中，我们给出了一个简短的证明，使用戈德曼公式的泊松括号的表示品种的曲面群到约化李群。
英文摘要：
Wolpert's cosine formula on Teichmüller space gives the Weil-Petersson Poisson bracket $\{l_α, l_β\}$ for geodesic length functions $l_α,l_β$ of closed curves $α,β$ as the sum of the cosines of the angle of intersection of the associated geodesics. This was recently generalized to Hitchin representations by Labourie. In this paper, we give a short proof of this generalization using Goldman's formula for the Poisson bracket on representation varieties of surface groups into reductive Lie groups.
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