Some closed hyperbolic 5-manifolds

TL;DR

This paper constructs explicit examples of closed arithmetic hyperbolic 5-manifolds, analyzes their properties like volume and Betti number, and introduces related manifolds with larger volume but simpler construction.

Contribution

It provides the first explicit construction of certain closed hyperbolic 5-manifolds and explores their geometric and topological properties.

Findings

Manifolds tessellated by over 117 million Coxeter simplicial prisms

Computed volume and Betti number of the constructed manifolds

Described a related family of manifolds with larger volume and simpler construction

Abstract

We give an explicit construction of a family of closed arithmetic hyperbolic 5-manifolds, tessellated by $117 964 800 = 512 \cdot 16 \cdot 14400$ copies of a Coxeter simplicial prism. We proceed to study various properties of these manifolds, such as the volume and the first Betti number. We also describe a related family of 5-manifolds with a larger volume, but a simpler construction.