论文标题
Anosov表示对紧凑型复杂歧管的统一化
Uniformization of compact complex manifolds by Anosov representations
论文作者
论文摘要
我们研究紧凑型歧管的统一问题，这些问题是通过Anosov同构图像作为复杂标志品种中域的商的商品。我们专注于具有“小”极限集的Anosov同态，如旗帜品种中的Riemannian Hausdorff codimension所衡量的那样。在这样的编成假设下，我们表明，在相关的紧凑型复杂歧管上，复杂结构的所有一阶变形都是通过Anosov同构的变形来实现的。有了一些温和的假设，我们表明角色品种在局部同词上映射到歧管的（广义）teichmüller空间。特别是，这提供了在Anosov较高复杂的半圣母层群体的Anosov同态的情况下，同时均匀化定理的局部类似物。
We study uniformization problems for compact manifolds that arise as quotients of domains in complex flag varieties by images of Anosov homomorphisms. We focus on Anosov homomorphisms with "small" limit sets, as measured by the Riemannian Hausdorff codimension in the flag variety. Under such a codimension hypothesis, we show that all first-order deformations of complex structure on the associated compact complex manifolds are realized by deformations of the Anosov homomorphism. With some mild additional hypotheses we show that the character variety maps locally homeomorphically to the (generalized) Teichmüller space of the manifold. In particular this provides a local analogue of the Bers Simultaneous Uniformization Theorem in the setting of Anosov homomorphisms to higher-rank complex semisimple Lie groups.
