Cusps of Hilbert modular varieties
Geometric Topology
2015-05-13 v1 Differential Geometry
Abstract
Motivated by a question of Hirzebruch on the possible topological types of cusp cross-sections of Hilbert modular varieties, we give a necessary and sufficient condition for a manifold M to be diffeomorphic to a cusp cross-section of a Hilbert modular variety. Specialized to Hilbert modular surfaces, this proves that every Sol 3-manifold is diffeomorphic to a cusp cross-section of a (generalized) Hilbert modular surface. We also deduce an obstruction to geometric bounding in this setting. Consequently, there exist Sol 3-manifolds that cannot arise as a cusp cross-section of a 1-cusped nonsingular Hilbert modular surface.
Keywords
Cite
@article{arxiv.0706.3580,
title = {Cusps of Hilbert modular varieties},
author = {D. B. McReynolds},
journal= {arXiv preprint arXiv:0706.3580},
year = {2015}
}