# Topological restrictions on Anosov representations

## TL;DR

This paper characterizes groups that admit various types of Anosov representations into special linear groups, providing bounds on their cohomological dimensions and characterizations of Benoist representations.

## Contribution

It offers new characterizations and bounds for groups admitting Anosov representations into SL(d,R), extending understanding of their topological and geometric properties.

## Key findings

- Characterization of groups admitting specific Anosov representations
- Bounds on cohomological dimensions of these groups
- Characterizations of Benoist representations

## Abstract

We characterize groups admitting Anosov representations into $\mathsf{SL}(3,\mathbb R)$, projective Anosov representations into $\mathsf{SL}(4,\mathbb R)$, and Borel Anosov representations into $\mathsf{SL}(4,\mathbb R)$. More generally, we obtain bounds on the cohomological dimension of groups admitting $P_k$-Anosov representations into $\mathsf{SL}(d,\mathbb R)$ and offer several characterizations of Benoist representations.