Anosov deformations of Barbot representations

TL;DR

This paper constructs a proper slice in the character variety of surface group representations into SL(3,R), showing these are Borel Anosov and describing associated fibered geometric structures.

Contribution

It introduces a new geometric slice in the character variety for Barbot representations linked to conformal structures on surfaces, proving their Borel Anosov property.

Findings

Constructed a proper slice in the character variety.

Proved the representations are Borel Anosov.

Described fibered geometric structures in flag space.

Abstract

We construct for each conformal structure on a closed orientable surface of genus at least 2 a proper slice in the character variety of representations of the associated surface group into SL(3,R) that belongs to the Barbot component and show that the corresponding representations are Borel Anosov. We describe a fibered geometric structure in the space of full flags associated with these representations.