Geometric structures and representations of discrete groups

TL;DR

This paper explores the connections between geometric structures on manifolds and the dynamics of discrete group representations into Lie groups, highlighting recent developments in understanding their interplay.

Contribution

It introduces new insights into how geometric structures relate to the dynamics of group representations at infinity.

Findings

Established links between geometric structures and group dynamics

Provided new frameworks for understanding representations of discrete groups

Highlighted recent advances in the field

Abstract

We describe recent links between two topics: geometric structures on manifolds in the sense of Ehresmann and Thurston, and dynamics "at infinity" for representations of discrete groups into Lie groups.