English

Cusps and Commensurability Classes of Hyperbolic 4-Manifolds

Geometric Topology 2023-11-15 v2

Abstract

There are six orientable, compact, flat 3-manifolds that can occur as cusp cross-sections of hyperbolic 4-manifolds. This paper provides criteria for exactly when a given commensurability class of arithmetic hyperbolic 4-manifolds contains a representative with a given cusp type. In particular, for three of the six cusp types, we provide infinitely many examples of commensurability classes that contain no manifolds with cusps of the given type; no such examples were previously known for any cusp type.

Keywords

Cite

@article{arxiv.2109.12172,
  title  = {Cusps and Commensurability Classes of Hyperbolic 4-Manifolds},
  author = {Connor Sell},
  journal= {arXiv preprint arXiv:2109.12172},
  year   = {2023}
}

Comments

24 pages, 6 figures. Clarified some definitions and theorem statements

R2 v1 2026-06-24T06:18:36.373Z