{"paper":{"title":"Dominating surface-group representations via Fock-Goncharov coordinates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Pabitra Barman, Subhojoy Gupta","submitted_at":"2024-05-24T09:23:57Z","abstract_excerpt":"Let $S$ be a punctured surface of negative Euler characteristic. We show that given a generic representation $\\rho:\\pi_1(S) \\rightarrow \\mathrm{PSL}_n(\\mathbb{C})$, there exists a positive representation $\\rho_0:\\pi_1(S) \\rightarrow \\mathrm{PSL}_n(\\mathbb{R})$ that dominates $\\rho$ in the Hilbert length spectrum as well as in the translation length spectrum, for the translation length in the symmetric space $\\mathbb{X}_n= \\mathrm{PSL}_n(\\mathbb{C})/\\mathrm{PSU}(n)$. Moreover, the $\\rho_0$-lengths of peripheral curves remain unchanged. The dominating representation $\\rho_0$ is explicitly descri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.15378","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.15378/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}