{"paper":{"title":"Mapping class group dynamics and the holonomy of branched affine structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.GT","authors_text":"Selim Ghazouani","submitted_at":"2016-07-25T09:18:56Z","abstract_excerpt":"We classify, up to few exceptions, the orbit closures of the $\\mathrm{Mod}(\\Sigma)$-action on the affine character variety $\\chi(\\mathrm{Aff}(\\mathbb{C}))$. We obtain from this classification that the only obstruction for a non-abelian representation $\\rho : \\pi_1 \\Sigma \\longrightarrow \\mathrm{Aff}(\\mathbb{C})$ to be the holonomy of a branched affine structure on $\\Sigma$ is to be Euclidean and not to have positive volume, where $\\Sigma$ is a closed oriented surface of genus $g \\geq 2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07185","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"}