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Cusp shapes of Hilbert-Blumenthal surfaces

Authors :
Alberto Verjovsky
Joseph Quinn
Publication Year :
2017
Publisher :
arXiv, 2017.

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.<br />Comment: 17 pages, 4 figures, 2 tables

Details

Database :
OpenAIRE
Accession number :
edsair.doi.dedup.....42629b7b27579688e889f3e71280c145
Full Text :
https://doi.org/10.48550/arxiv.1711.02418