Rigidity of partially hyperbolic dynamical systems and actions of solvable Lie groups

我给出了三维流形上二维非阿贝尔李群的局部自由作用的完整分类，这是一个五十年来一直未解决的问题。并构造了动作的变形空间。对于高维的类似动作，我推测它们类似于低维的ASE是灵活的。然而，事实证明，动作在更高的维度上表现出刚性。根据轨道叶的叶向上同调，我还模拟了关于可解李群的局部自由作用的参数刚性的一个自然猜想。

I gave a complete classification of locally free actions of the wo-dimensional non-abelian Lie group on three-manifolds, which was a open problem for hirty years. I also constructed the deformation space of the actions. For analogous actions n higher dimension, I conjectured that they are flexible similar to the low-dimensional ase. However, it turned out that the actions exhibits rigidity in higher-dimension. I also ormulated a natural conjecture on parameter rigidity of locally free actions of solvable Lie roups in terms of the leafwise cohomology of the orbit foliations