{"paper":{"title":"Collapsed manifolds with local Ricci bounded covering geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Xiaochun Rong","submitted_at":"2022-11-18T02:55:04Z","abstract_excerpt":"For $\\rho, v>0$, we say that an $n$-manifold $M$ satisfies local $(\\rho,v)$-bound Ricci covering geometry, if Ricci curvature $\\text{Ric}_M\\ge -(n-1)$, and for all $x\\in M$, $\\text{vol}(B_\\rho(\\tilde x))\\ge v>0$, where $\\tilde x$ is an inverse image of $x$ on the (local) Riemannian universal cover of the $\\rho$-ball at $x$.\n  In this paper, we extend the nilpotent fiber bundle theorem of Cheeger-Fukaya-Gromov on a collapsed $n$-manifold $M$ of bounded sectional curvature to $M$ of a local $(\\rho,v)$-bound Ricci covering geometry, and $M$ is close to a non-collapsed Riemannian manifold of lower"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.09998","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2211.09998/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"}