Coloured symmetries of rational homology 3-spheres that cover right-angled polytopes

TL;DR

This paper investigates the symmetries of hyperbolic rational homology 3-spheres derived from right-angled polytopes, focusing on their existence, absence, and construction of symmetries that preserve tessellations.

Contribution

It provides a systematic study of symmetries in these manifolds and introduces methods to create colorings with specified symmetry properties.

Findings

Identified conditions for the existence of symmetries in these manifolds.

Developed techniques to construct colorings with desired symmetries.

Analyzed the impact of symmetries on the tessellation structure.

Abstract

In the present paper we study hyperbolic manifolds that are rational homology 3-spheres obtained by colouring of right--angled polytopes. We study the existence (or absence) of different kinds of symmetries of rational homology spheres that preserve the tessellation of the manifold into polytopes. We also describe how to create colourings with given symmetries.