Dubrovin-Ugaglia Poisson流形中作为退化辛叶的Teichmüller空间
Teichmüller spaces as degenerated symplectic leaves in Dubrovin--Ugaglia Poisson manifolds
摘要：
本文研究了具有$s=1,2$洞的亏格为$g$的黎曼曲面$Σ_{g,s,0}$上测地长度函数之间的Goldman括号，以及具有一个洞的黎曼球面$Σ_{0,1,n}$上的测地长度函数之间的Goldman括号和具有二阶$n$轨点的测地长度函数之间的Goldman括号.我们证明了相应的Teichmüller空间$\mathcal T_{g,s,0}$和$\mathcal T_{0,1,n}$被实现为对角线上为1的上三角矩阵$S$的Dubrovin-Ugaglia Poisson代数中退化辛叶的实切片.
英文摘要：
In this paper we study the Goldman bracket between geodesic length functions both on a Riemann surface $Σ_{g,s,0}$ of genus $g$ with $s=1,2$ holes and on a Riemann sphere $Σ_{0,1,n}$ with one hole and $n$ orbifold points of order two. We show that the corresponding Teichmüller spaces $\mathcal T_{g,s,0}$ and $\mathcal T_{0,1,n}$ are realised as real slices of degenerated symplectic leaves in the Dubrovin--Ugaglia Poisson algebra of upper--triangular matrices $S$ with 1 on the diagonal.
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