{"paper":{"title":"Complete 4-manifolds with uniformly 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":"2009-12-30T07:44:42Z","abstract_excerpt":"We prove the following result: Let $(X,g_0)$ be a complete, connected 4-manifold with uniformly positive isotropic curvature and with bounded geometry. Then there is a finite collection $\\mathcal{F}$ of manifolds of the form $\\mathbb{S}^3 \\times \\mathbb{R} /G$, where $G$ is a fixed point free discrete subgroup of the isometry group of the standard metric on $\\mathbb{S}^3\\times \\mathbb{R}$, such that $X$ is diffeomorphic to a (possibly infinite) connected sum of copies of $\\mathbb{S}^4,\\mathbb{RP}^4$ and/or members of $\\mathcal{F}$. This extends recent work of Chen-Tang-Zhu and Huang. We also e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.5405","kind":"arxiv","version":13},"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"}