{"paper":{"title":"Riemann surfaces and the geometrization of 3-manifolds","license":"","headline":"","cross_cats":["math.CV"],"primary_cat":"math.GT","authors_text":"Curt McMullen","submitted_at":"1992-10-01T00:00:00Z","abstract_excerpt":"About a decade ago Thurston proved that a vast collection of 3-manifolds carry metrics of constant negative curvature. These manifolds are thus elements of {\\em hyperbolic geometry}, as natural as Euclid's regular polyhedra. For a closed manifold, Mostow rigidity assures that a hyperbolic structure is unique when it exists, so topology and geometry mesh harmoniously in dimension 3.\n  This remarkable theorem applies to all 3-manifolds, which can be built up in an inductive way from 3-balls, i.e., {\\em Haken} manifolds. Thurston's construction of a hyperbolic structure is also inductive. At the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9210224","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"}