On Pappus and Anosov Representations of the Modular Group
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911686121750528 |
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| author | Schwartz, Richard Evan |
| author_facet | Schwartz, Richard Evan |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_15317 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Pappus and Anosov Representations of the Modular Group Schwartz, Richard Evan Geometric Topology 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. |
| title | On Pappus and Anosov Representations of the Modular Group |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2605.15317 |