{"paper":{"title":"Deformations of Fuchsian AdS representations are Quasi-Fuchsian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math.DG"],"primary_cat":"math.RT","authors_text":"Thierry Barbot (LANLG)","submitted_at":"2013-01-18T07:31:18Z","abstract_excerpt":"Let $\\Gamma$ be a finitely generated group, and let $\\op{Rep}(\\Gamma, \\SO(2,n))$ be the moduli space of representations of $\\Gamma$ into $\\SO(2,n)$ ($n \\geq 2$). An element $\\rho: \\Gamma \\to \\SO(2,n)$ of $\\op{Rep}(\\Gamma, \\SO(2,n))$ is \\textit{quasi-Fuchsian} if it is faithful, discrete, preserves an acausal subset in the conformal boundary $\\Ein_n$ of the anti-de Sitter space; and if the associated globally hyperbolic anti-de Sitter space is spatially compact - a particular case is the case of \\textit{Fuchsian representations}, i.e. composition of a faithfull, discrete and cocompact represent"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4309","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"}