{"paper":{"title":"The link surgery of $S^2\\times S^2$ and Scharlemann's manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Motoo Tange","submitted_at":"2010-11-24T07:10:56Z","abstract_excerpt":"Fintushel-Stern's knot surgery gave many pairs of exotic manifolds, which are homeomorphic but non-diffeomorphic. We show that if an elliptic fibration has two parallel, oppositely oriented vanishing circles (for example $S^2\\times S^2$ or Matsumoto's $S^4$), then the knot surgery gives rise to standard manifolds. The diffeomorphism can give an alternative proof that Scharlemann's manifold is standard (originally by Akbulut [Ak1])."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.5308","kind":"arxiv","version":3},"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"}