{"paper":{"title":"Gromov-Hausdorff Limits of Aspherical Manifolds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Xiaochun Rong","submitted_at":"2025-03-29T14:58:37Z","abstract_excerpt":"Let $X$ be a compact Gromov-Hausdorff limit space of a collapsing sequence of compact $n$-manifolds, $M_i$, of Ricci curvature $\\text{Ric}_{M_i}\\ge -(n-1)$ and all points in $M_i$ are $(\\delta,\\rho)$-local rewinding Reifenberg points, or sectional curvature $\\text{sec}_{M_i}\\ge -1$, respectively. We conjecture that if $M_i$ is an aspherical manifold of fundamental group satisfying a certain condition (e.g., a nilpotent group), then $X$ is a differentiable, or topological aspherical manifold, respectively. A main result in this paper asserts that if $M_i$ a diffeomorphic or homeomorphic to a ni"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.23107","kind":"arxiv","version":2},"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/2503.23107/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"}