{"paper":{"title":"Super-maximal representations from fundamental groups of punctured surfaces to $\\mathrm{PSL}(2,\\mathbb{R})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.GR"],"primary_cat":"math.GT","authors_text":"Bertrand Deroin, Nicolas Tholozan","submitted_at":"2016-04-01T17:00:34Z","abstract_excerpt":"We study a particular class of representations from the fundamental groups of punctured spheres $\\Sigma_{0,n}$ to the group $\\text{PSL} (2,\\mathbb R)$ (and their moduli spaces), that we call \\emph{super-maximal}. Super-maximal representations are shown to be \\emph{totally non hyperbolic}, in the sense that every simple closed curve is mapped to a non hyperbolic element. They are also shown to be \\emph{geometrizable} (appart from the reducible super-maximal ones) in the following very strong sense : for any element of the Teichm\\\"uller space $\\mathcal T_{0,n}$, there is a unique holomorphic equ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.00330","kind":"arxiv","version":1},"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"}