{"paper":{"title":"Dominating surface group representations and deforming closed AdS 3-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.RT"],"primary_cat":"math.GT","authors_text":"Nicolas Tholozan","submitted_at":"2014-03-28T18:36:17Z","abstract_excerpt":"In a previous paper by Deroin-Tholozan, the authors construct a map $\\mathbf{\\Psi}_\\rho$ from the Teichm\\\"uller space of $S$ to itself and prove that, when $M$ has sectional curvature $\\leq -1$, the image of $\\mathbf{\\Psi}_\\rho$ lies (almost always) in the domain $\\mathrm{Dom}(\\rho)$ of Fuchsian representations stricly dominating $\\rho$. Here we prove that $\\mathbf{\\Psi}_\\rho: \\mathrm{Teich}(S) \\to \\mathrm{Dom}(\\rho)$ is a homeomorphism. As a consequence, we are able to describe the topology of the deformation space of anti-de Sitter structures on closed 3-manifolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7479","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"}