{"paper":{"title":"The Riemann-Hilbert mapping for $\\mathfrak{sl}_2$ -systems over genus two curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CV","authors_text":"Bertrand Deroin, Frank Loray, Gabriel Calsamiglia, Viktoria Heu","submitted_at":"2016-02-06T16:30:06Z","abstract_excerpt":"We prove in two different ways that the monodromy map from the space of irreducible $\\mathfrak{sl}_2$-differential-systems on genus two Riemann surfaces, towards the character variety of $\\mathrm{SL}_2$-representations of the fundamental group, is a local diffeomorphism. This is motivated by a question raised by \\'Etienne Ghys about Margulis' problem: existence of curves of negative Euler characteristic in compact quotients of $\\mathrm{SL}_2(\\mathbb{C})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02273","kind":"arxiv","version":4},"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"}