{"paper":{"title":"Homotopy Hyperbolic 3-Manifolds are Hyperbolic","license":"","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"David Gabai, G. Robert Meyerhoff, Nathaniel Thurston","submitted_at":"1996-09-13T00:00:00Z","abstract_excerpt":"This paper introduces a rigorous computer-assisted procedure for analyzing hyperbolic 3-manifolds. This technique is used to complete the proof of several long-standing rigidity conjectures in 3-manifold theory as well as to provide a new lower bound for the volume of a closed orientable hyperbolic 3-manifold.\n  We prove the following result:\n  \\it\\noindent Let $N$ be a closed hyperbolic 3-manifold. Then \\begin{enumerate} \\item[(1)] If $f\\colon M \\to N$ is a homotopy equivalence where $M$ is a closed irreducible 3-manifold, then $f$ is homotopic to a homeomorphism. \\item[(2)] If $f,g\\colon M\\t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9609207","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"}