Compact Clifford-Klein forms -- geometry, topology and dynamics

TL;DR

This paper surveys recent advances in the study of compact Clifford-Klein forms of homogeneous spaces, emphasizing approaches from topology, geometry, and dynamics, and also discusses moduli spaces of these forms.

Contribution

It provides a comprehensive overview of recent results and methods related to compact Clifford-Klein forms, integrating multiple mathematical perspectives.

Findings

Summarizes key results in topology, geometry, and dynamics of compact forms.

Highlights recent progress in understanding moduli spaces of compact forms.

Organizes diverse approaches to the problem in a unified survey.

Abstract

We survey results on compact Clifford-Klein forms of homogeneous spaces, with a focus on recent contributions and organized around approaches via topology, geometry and dynamics. In addition, we survey results on moduli spaces of compact forms.