Representations of the modular group into the isometries of SL(3,R)/SO(3)

Abstract

We describe the topology of the variety of characters of the modular group ${\mathrm{PSL}}_2(\mathbb{Z})$ into the isometry group of the symmetric space ${\mathrm{SL}}_3(\mathbb{R})/\mathrm{SO}(3)$. This topology is determined in terms of the fixed point sets of the generators of the modular group. We also find Anosov representations on each nontrivial component.

43 pages, 15 figures. V2 acknowledges previous work. V3 has been expanded and computes the whole variety of characters. V4: I forgot to update the abstract in V3, the file is the same