Nil 3-manifolds and cusps of complex hyperbolic surfaces
Geometric Topology
2024-11-28 v1 Differential Geometry
Group Theory
Abstract
McReynolds showed that every compact Nil 3-manifold occurs as the cusp cross-section of some arithmetic complex hyperbolic 2-manifold. We classify which commensurability classes of cusped, arithmetic, complex hyperbolic 2-manifolds admit cusps with cross-section homeomorphic to a given compact Nil 3-manifold. In particular, there are some Nil 3-manifolds which occur as cusps in every such commensurability class, and some which only occur in a single commensurability class. We also show that every compact Nil 3-manifold occurs as the cusp cross-section of some non-arithmetic complex hyperbolic 2-manifold.
Keywords
Cite
@article{arxiv.2411.15345,
title = {Nil 3-manifolds and cusps of complex hyperbolic surfaces},
author = {Julien Paupert and Connor Sell},
journal= {arXiv preprint arXiv:2411.15345},
year = {2024}
}