{"paper":{"title":"Compact manifolds of dimension $n\\geq 12$ 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":"2019-09-26T17:20:19Z","abstract_excerpt":"We prove the following result: Let $(M,g_0)$ be a compact manifold of dimension $n\\geq 12$ with positive isotropic curvature. Then $M$ is diffeomorphic to a spherical space form, or the total space of an orbifiber bundle over $\\mathbb{S}^1$ or $\\mathcal{I}$ with generic fiber diffeomorphic to $\\mathbb{S}^{n-1}/\\Gamma$ such that the total space admits a metric with positive isotropic curvature, where $\\Gamma$ is a finite subgroup of $O(n)$ acting freely on $\\mathbb{S}^{n-1}$, and $\\mathcal{I}$ is the one dimensional closed orbifold with two singular points both with local group $\\mathbb{Z}_2$ a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.12265","kind":"arxiv","version":22},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1909.12265/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}