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arXiv · 1711.02418

Cusp shapes of Hilbert-Blumenthal surfaces

Joseph Quinn·Alberto Verjovsky
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Abstract

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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Joseph Quinn, Alberto Verjovsky. 2019-06-27. Cusp shapes of Hilbert-Blumenthal surfaces. https://doi.org/10.1007/s10711-019-00474-w

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