Hilbert-Blumenthal曲面的尖点形状
Cusp shapes of Hilbert-Blumenthal surfaces
摘要：
引入了实二次域K=Q（sqrt n）上Hilbert模群的尖点稳定子的一个新的基本区.这被构造为极大幂幺群的Dirichlet域在双平面的叶上的并。该区域是正实数与K的整数环中格的变形所形成的三维塔的笛卡儿积，并明确了尖点截面的Sol 3-流形结构和Anosov同构.我们包括计算机生成的图像和数据说明各种例子。
英文摘要：
We introduce a new fundamental domain for the cusp stabilizer of a Hilbert modular group over a real quadratic field K=Q(sqrt n). This is constructed as the union of Dirichlet domains for the maximal unipotent group, over the leaves in a foliation of the biplane. The region is the Cartesian product of the positive reals with a 3-dimensional tower formed by deformations of lattices in the ring of integers of K, and makes explicit the cusp cross section's Sol 3-manifold structure and Anosov diffeomorphism. We include computer generated images and data illustrating various examples.
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