Cusp shapes of Hilbert–Blumenthal surfaces
Cusp shapes of Hilbert–Blumenthal surfaces
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希尔伯特-布卢门撒尔曲面的尖点形状
作者：
Joseph A. Quinn;A. Verjovsky
我们引入了一个新的基本域$$\mathscr{R}_n$$Rn，用于实二次域$$K=\mathbb{q}(\Γ{n})$$K=q(N)上的Hilbert模群$$\Gamma$$的尖点稳定子.它被构造为极大幂等群的Dirichlet域的并，它位于叶上的$$\数学{H}^2\数学\数学{H}^2$$H2×H2的叶层上。区域$$\mathscr{R}_n$$Rn是$\mathbb{R}^+$$R+与由整数环$$\mathbb{Z}_K$$Z K中的格点形变形成的三维塔形$$\数学{T}_n$$Tn的乘积，并显式地显示了尖端截面的SOL3-流形结构和Anosov微分同胚.我们包括计算机生成的图像和数据，以说明各种例子。
We introduce a new fundamental domain $$\mathscr {R}_n$$ R n for a cusp stabilizer of a Hilbert modular group $$\Gamma $$ Γ over a real quadratic field $$K=\mathbb {Q}(\sqrt{n})$$ K = Q ( n ) . This is constructed as the union of Dirichlet domains for the maximal unipotent group, over the leaves in a foliation of $$\mathcal {H}^2\times \mathcal {H}^2$$ H 2 × H 2 . The region $$\mathscr {R}_n$$ R n is the product of $$\mathbb {R}^+$$ R + with a 3-dimensional tower $$\mathcal {T}_n$$ T n formed by deformations of lattices in the ring of integers $$\mathbb {Z}_K$$ Z 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.