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arXiv · 2605.15317

On Pappus and Anosov Representations of the Modular Group

Richard Evan Schwartz
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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.

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Richard Evan Schwartz. 2026-05-14. On Pappus and Anosov Representations of the Modular Group. https://arxiv.org/abs/2605.15317

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