A primer on the (2+1) Einstein universe

TL;DR

This paper explores the geometric and causal structure of the (2+1)-dimensional Einstein universe, highlighting its connections with symplectic geometry and its role as a boundary of anti-de Sitter space.

Contribution

It develops the synthetic geometry of the (2+1) Einstein universe focusing on homogeneous submanifolds and causal structure, emphasizing its relation to symplectic geometry.

Findings

Characterization of the Einstein universe's homogeneous submanifolds

Analysis of the causal structure in (2+1) dimensions

Connections established between Einstein universe geometry and symplectic geometry

Abstract

The Einstein universe is the conformal compactification of Minkowski space. It also arises as the ideal boundary of anti-de Sitter space. The purpose of this article is to develop the synthetic geometry of the Einstein universe in terms of its homogeneous submanifolds and causal structure, with particular emphasis on dimension $2 + 1$, in which there is a rich interplay with symplectic geometry.