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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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":true,"formal_links_present":true},"canonical_record":{"source":{"id":"2605.15317","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2026-05-14T18:31:01Z","cross_cats_sorted":[],"title_canon_sha256":"3ff3758b589074adc08b293f9ba9d2acf004fa5684603eee92b2c9bc34718cbe","abstract_canon_sha256":"d4a0f0875d5ec9eaf55cc11d3549b06e7c4115f74b525c792a20b18291f0b3c5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:00:52.349289Z","signature_b64":"CSzLM4gV7w5DiMyoij4j/NlEyN9AcdIhGwEvCflZ4EGCMGF5jUO11QX95CNGRG3CBvvCW375RJEux7Y0Dfk6BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e62311568cce5a6b6dc5d4584c6c5b860c6a77d58bac98543b12c8baf25cd002","last_reissued_at":"2026-05-20T00:00:52.348685Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:00:52.348685Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Pappus and Anosov Representations of the Modular Group","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The Barbot component of discrete faithful representations of the modular group into Isom(SL3(R)/SO(3)) is homeomorphic to R² × [0, ∞).","cross_cats":[],"primary_cat":"math.GT","authors_text":"Richard Evan Schwartz","submitted_at":"2026-05-14T18:31:01Z","abstract_excerpt":"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."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"DFR has a component B, the Barbot component, that is homeomorphic to R² × [0,∞). 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