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Cusp shapes of Hilbert-Blumenthal surfaces
- 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
- Subjects :
- Cusp (singularity)
Mathematics - Number Theory
010102 general mathematics
Geometric Topology (math.GT)
11F41, 57N16, 11R04
Unipotent
01 natural sciences
Tower (mathematics)
Ring of integers
Combinatorics
Mathematics - Geometric Topology
Fundamental domain
Modular group
Product (mathematics)
0103 physical sciences
FOS: Mathematics
Quadratic field
010307 mathematical physics
Geometry and Topology
Number Theory (math.NT)
0101 mathematics
Mathematics
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....42629b7b27579688e889f3e71280c145
- Full Text :
- https://doi.org/10.48550/arxiv.1711.02418