On deformations of free groups in compact Lie groups

李群上交叉同态的变形

Deformations of crossed homomorphisms on Lie groups

本文研究了李群上交叉同态的变形，通过上同调分析其刚性性质，并探讨了与李代数上同调的关系。

Deformations and rigidity of lattices in solvable Lie groups

Let $G$ be a simply connected, solvable Lie group and $Γ$ a lattice in $G$. The deformation space $\mathcal{D}(Γ,G)$ is the orbit space associated to the action of $\Aut(G)$ on the space $\mathcal{X}(Γ,G)$ of all lattice embeddings of $Γ$ into $G$. Our main result generalises the classical rigidity theorems of Mal'tsev and Saitô for lattices in nilpotent Lie groups and in solvable Lie groups of real type. We prove that the deformation space of every Zariski-dense lattice $Γ$ in $G$ is finite and Hausdorff, provided that the maximal nilpotent normal subgroup of $G$ is connected. This implies th…

李群胚作用的轨道固定形变空间

The orbit-fixing deformation spaces of an action of a Lie groupoid

本文通过模仿曲面Teichmüller空间重新表述了李群胚作用的形变空间，推广至可能非局部自由的作用与非紧流形，证明了上链刚性意味着形变空间为单点，并计算了$\mathop{\mathrm{PSL}}(2,\mathbb{R})$的具体形变空间。