{"paper":{"title":"Lower Ricci Curvature and Nonexistence of Manifold Structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Aaron Naber, Erik Hupp, Kai-Hsiang Wang","submitted_at":"2023-08-07T20:52:10Z","abstract_excerpt":"It is known that a limit $(M^n_j,g_j)\\to (X^k,d)$ of manifolds $M_j$ with uniform lower bounds on Ricci curvature must be $k$-rectifiable for some unique $\\dim X:= k\\leq n = \\dim M_j$. It is also known that if $k=n$, then $X^n$ is a topological manifold on an open dense subset, and it has been an open question as to whether this holds for $k<n$.\n  Consider now any smooth complete $4$-manifold $(X^4,h)$ with $\\text{Ric}>\\lambda$ and $\\lambda\\in \\mathbb{R}$. Then for each $\\epsilon>0$ we construct a complete $4$-rectifiable metric space $(X^4_\\epsilon,d_\\epsilon)$ with $d_{GH}(X^4_\\epsilon,X^4)<"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.03909","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/2308.03909/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"}