How to see the eight Thurston geometries

TL;DR

This paper surveys the history and classification of Thurston's eight geometries and discusses recent visualization techniques for three-dimensional manifolds related to the Geometrization Conjecture.

Contribution

It provides a comprehensive overview of the geometrization conjecture, Thurston's geometries, and introduces recent immersive visualization methods.

Findings

Historical overview of the geometrization conjecture

Classification of Thurston's eight geometries

Introduction to immersive visualization techniques

Abstract

In this expository paper, we present a survey about the history of the geometrization conjecture and the background material on the classification of Thurston's eight geometries. We also discuss recent techniques for immersive visualization of relevant three-dimensional manifolds in the context of the Geometrization Conjecture.