On the Anosov character of the Pappus–Schwartz representations

Abstract

In the paper Pappus's Theorem and The Modular Group (1993) [4], R.E. Schwartz observed that the classical Pappus theorem gives rise to an action of the modular group on the space of marked boxes. He inferred from this a 2-dimensional family of faithful representations of the modular group into the group of projective symmetries. These representations have a dynamical behavior very similar to the one of Anosov representations, even if they are never Anosov themselves. In this note, we announce the main result of V. Pardini Valério (2016) [3], which elucidates this Anosov character of the Schwartz representations by proving that their restrictions to the index-2 subgroup are limits of Anosov representations.