{"paper":{"title":"Pappus Theorem, Schwartz Representations and Anosov Representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT","math.RT"],"primary_cat":"math.DS","authors_text":"Gye-Seon Lee, Thierry Barbot, Viviane Pardini Val\\'erio","submitted_at":"2016-10-13T12:37:36Z","abstract_excerpt":"In the paper \"Pappus's theorem and the modular group\", R. Schwartz constructed a 2-dimensional family of faithful representations $\\rho_\\Theta$ of the modular group $\\mathrm{PSL}(2,\\mathbb{Z})$ into the group $\\mathscr{G}$ of projective symmetries of the projective plane via Pappus Theorem. The image of the unique index 2 subgroup $\\mathrm{PSL}(2,\\mathbb{Z})_o$ of $\\mathrm{PSL}(2,\\mathbb{Z})$ under each representation $\\rho_\\Theta$ is in the subgroup $\\mathrm{PGL}(3,\\mathbb{R})$ of $\\mathscr{G}$ and preserves a topological circle in the flag variety, but $\\rho_\\Theta$ is not Anosov. In her PhD"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04049","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}