Thurston h-原理与Poisson结构的柔度

图斯通定理周围灵活性和退化性

Flexibility and degeneracy around a theorem of Thurston

本文提出两种与图斯通定理相关的灵活退化构造，探讨了Teichmüller空间中测地线的稳定性及表示极限锥的结构。

泊松几何中的刚与柔

Rigidity and Flexibility in Poisson Geometry

我们讨论了泊松几何中的几个刚性和柔性现象。

Symplectic structures on Teichmüller spaces $\mathfrak T_{g,s,n}$ and cluster algebras

We recall the fat-graph description of Riemann surfaces $Σ_{g,s,n}$ and the corresponding Teichmüller spaces $\mathfrak T_{g,s,n}$ with $s>0$ holes and $n>0$ bordered cusps in the hyperbolic geometry setting. If $n>0$, we have a bijection between the set of Thurston shear coordinates and Penner's $λ$-lengths and we can induce, on the one hand, the Poisson bracket on $λ$-lengths from the Poisson bracket on shear coordinates introduced by V.V.Fock in 1997 and, on the other hand, a symplectic structure $Ω_{\text{WP}}$ on the set of extended shear coordinates from Penner's symplectic structure on …

Geometric structures and Lie algebroids

In this thesis we study geometric structures from Poisson and generalized complex geometry with mild singular behavior using Lie algebroids. The process of lifting such structures to their Lie algebroid version makes them less singular, as their singular behavior is incorporated in the anchor of the Lie algebroid. We develop a framework for this using the concept of a divisor, which encodes the singularities, and show when structures exhibiting such singularities can be lifted to a Lie algebroid built out of the divisor. Once one has successfully lifted the structure, it becomes possible to st…