Cusps and Commensurability Classes of Hyperbolic 4-Manifolds

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.

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

References in corpus (5)

• Describing the platycosms
• Systoles of hyperbolic 4-manifolds
• Cusps of hyperbolic 4-manifolds and rational homology spheres
• Embedding closed hyperbolic 3-manifolds in small volume hyperbolic 4-manifolds
• On the coverings of Hantzsche-Wendt manifold