Non-isometric hyperbolic 3-orbifolds with the same topological type and volume

TL;DR

This paper constructs pairs of non-isometric hyperbolic 3-orbifolds that share the same topological type and volume, demonstrating new examples in hyperbolic geometry.

Contribution

It provides explicit examples of non-isometric hyperbolic 3-orbifolds with identical volume and topological type, expanding understanding of hyperbolic orbifold classification.

Findings

Constructed pairs of non-isometric hyperbolic 3-orbifolds

Shared topological type and volume

Orbifolds are mapping tori of genus 2 pseudo-Anosov maps

Abstract

We construct pairs of non-isometric hyperbolic 3-orbifolds with the same topological type and volume. Topologically these orbifolds are mapping tori of pseudo-Anosov maps of the surface of genus 2, with singular locus a fibred (hyperbolic) link with five components.