Infinitely many arithmetic hyperbolic rational homology 3-spheres that bound geometrically

TL;DR

This paper presents the first known examples of arithmetic hyperbolic 3-manifolds that are rational homology spheres and can bound hyperbolic 4-manifolds, either compact or with cusps.

Contribution

It introduces the first explicit examples of such 3-manifolds with these properties, expanding understanding of their geometric and topological relationships.

Findings

Existence of arithmetic hyperbolic 3-manifolds that bound hyperbolic 4-manifolds

Construction of examples that are rational homology spheres

Boundaries include both compact and cusped hyperbolic 4-manifolds

Abstract

In this paper we provide the first examples of arithmetic hyperbolic 3-manifolds that are rational homology spheres and bound geometrically either compact or cusped hyperbolic 4-manifolds.