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Then $X$ is diffeomorphic to $\\mathbb{S}^4$, or $\\mathbb{RP}^4$, or $\\mathbb{S}^3\\times \\mathbb{S}^1$, or $\\mathbb{S}^3\\widetilde{\\times} \\mathbb{S}^1$, or a possibly infinite connected sum of them.\n  This extends work of Hamilton and Chen-Zhu to the noncompact case. The proof uses Ricci flow with surgery on complete 4-manifolds, and is inspired by recent work of Bessi$\\grave{e}$res, Besson an"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1108.2918","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-08-15T01:59:57Z","cross_cats_sorted":[],"title_canon_sha256":"000b4a1d5848f91fd2f35bf5e8f62eb26648af8fefa367a71befb030c486dbd3","abstract_canon_sha256":"126bb89c0bf4468bd0a9b1c1f1fce6292e4a4e1c9915e8b447e301a0ae2443da"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:28.746015Z","signature_b64":"Pn8VTc0YB26Kzyxq25uVeyzKgY9UOvHORrfCLkG+ev6xkQoZ6Rxte3mWrxfs50Ry9t0GoMHY4aKu9tKc9P/tAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"192afc84b99661019c3c9573a78c41cdcb3ba2773c15e5d80c6c6d666290ea80","last_reissued_at":"2026-05-18T04:14:28.745389Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:28.745389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ricci flow on open 4-manifolds with positive isotropic curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Hong Huang","submitted_at":"2011-08-15T01:59:57Z","abstract_excerpt":"In this note we prove the following result: Let $X$ be a complete, connected 4-manifold with uniformly positive isotropic curvature, with bounded geometry and with no essential incompressible space form. 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