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

给出了三维流形上二维非交换李群的局部自由作用的一个完全分类，这是一个多年来的公开问题。并构造了动作的变形空间。对于高维的类似作用，我证明了它们是灵活的类似于低维的ase。然而，事实证明，行动表现出刚性在更高的维度。我还利用轨道叶理的叶向上同调，给出了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