5-dimensional geometries I: the general classification

TL;DR

This paper introduces a comprehensive classification of 5-dimensional Thurston geometries, revealing new phenomena like uncountable families of geometries, and sets the foundation for a detailed three-part series.

Contribution

It provides the first complete classification of 5-dimensional Thurston geometries, including novel phenomena not seen in lower dimensions.

Findings

Full list of 5D Thurston geometries

Identification of uncountable families of geometries

Outline of classification methodology

Abstract

This paper is the first of a 3-part series that classifies the 5-dimensional Thurston geometries. The present paper (part 1 of 3) summarizes the general classification, giving the full list, an outline of the method, and some illustrative examples. This includes phenomena that have not appeared in lower dimensional geometries, such as an uncountable family of geometries.