Kirby diagrams and the Ratcliffe-Tschantz hyperbolic 4-manifolds

TL;DR

This paper presents a method to construct Kirby diagrams for a broad class of finite volume hyperbolic 4-manifolds, facilitating their topological analysis.

Contribution

It introduces a systematic approach to visualize and study Ratcliffe-Tschantz hyperbolic 4-manifolds using Kirby diagrams, which was not previously established.

Findings

Kirby diagrams successfully constructed for many hyperbolic 4-manifolds

Enhanced understanding of the topology of Ratcliffe-Tschantz manifolds

Potential for further topological and geometric analysis

Abstract

We show how to construct a Kirby diagram for a large class of finite volume hyperbolic 4-manifolds constructed by J. Ratcliffe and S. Tschantz.