Cyclic generalizations of two hyperbolic icosahedral manifolds

TL;DR

This paper explores two families of three-dimensional manifolds that generalize hyperbolic icosahedral manifolds through cyclic coverings, analyzing their topological and geometric properties such as fundamental groups and volumes.

Contribution

It introduces new cyclic generalizations of hyperbolic icosahedral manifolds and investigates their covering properties, fundamental groups, and hyperbolic volumes.

Findings

Identification of covering properties of the manifolds

Determination of fundamental groups

Calculation of hyperbolic volumes

Abstract

We discuss two families of closed orientable three-dimensional manifolds which arise as cyclic generalizations of two hyperbolic icosahedral manifolds listed by Everitt. Everitt's manifolds are cyclic coverings of the lens space $L_{3,1}$ branched over some 2-component links. We present results on covering properties, fundamental groups, and hyperbolic volumes of the manifolds belonging to these families.