A Classification of subgroups of SL(4,R) Isomorphic to R^3 and Generalized Cusps in Projective 3 Manifolds

TL;DR

This paper classifies all R^3 subgroups of PGL(4,R) up to conjugacy and identifies four families of generalized cusps in 3-dimensional projective manifolds, advancing understanding of geometric structures.

Contribution

It provides a complete classification of R^3 subgroups in PGL(4,R) and describes the four types of generalized cusps in dimension 3.

Findings

Four families of generalized cusps identified

Complete classification of R^3 subgroups in PGL(4,R)

Enhanced understanding of 3D projective geometries

Abstract

This paper uses work of Haettel to classify all subgroups of PGL(4,R) isomorphic to (R^3 , +), up to conjugacy. We use this to show there are 4 families of generalized cusps up to projective equivalence in dimension 3.