The Auslander conjecture for NIL-affine crystallographic groups

幂零群的全纯多项式晶体作用

Holomorphic polynomial crystallographic actions of nilpotent groups

本文证明每个带有左不变幂零复结构的单连通幂零李群双全纯于C^n，并通过指数坐标中的多项式映射显式构造该双全纯映射，从而得到该李群中的格点通过全纯多项式自同构在C^n上自由、不连续且余紧致的作用。

Deformation Spaces for Affine Crystallographic Groups

We develop the foundations of the deformation theory of compact complete affine space forms and affine crystallographic groups. Using methods from the theory of linear algebraic groups we show that these deformation spaces inherit an algebraic structure from the space of crystallographic homomorphisms. We also study the properties of the action of the homotopy mapping class groups on deformation spaces. In our context these groups are arithmetic groups, and we construct examples of flat affine manifolds where every finite group of mapping classes admits a fixed point on the deformation space. …