On Pappus and Anosov Representations of the Modular Group

Richard Evan Schwartz

On Pappus and Anosov Representations of the Modular Group

Geometric Topology 2026-05-18 v1

Authors: Richard Evan Schwartz

Abstract

Let $X=SL_3(\R)/SO(3)$ . Let $\cal DFR$ be the space of discrete faithful representations of the modular group into ${\rm Isom\/}(X)$ which map the order $2$ generator to an isometry with a unique fixed point. In this paper, we prove that $\cal DFR$ has a component $\cal B$ , the so-called Barbot component, that is homeomorphic to $\R^2 \times [0,\infty)$ . The boundary of $\cal B$ parametrizes the Pappus representations and the interior consists of Anosov representations.

Keywords

Pappus representations Anosov representations modular group discrete faithful representations isometry group Barbot component

Cite

@article{arxiv.2605.15317,
  title  = {On Pappus and Anosov Representations of the Modular Group},
  author = {Richard Evan Schwartz},
  journal= {arXiv preprint arXiv:2605.15317},
  year   = {2026}
}

Comments

This is an edited and improved subset of a very long paper of mine, arXiv:2412.18547. In this shorter paper I isolate one of the main results and give a self-contained proof. I also take the opportunity to fix a few glitches and add some helpful details. Computer assisted - Mathematica files downloadable from my website

On Pappus and Anosov Representations of the Modular Group

Abstract

Keywords

Cite

Comments

Related papers