{"paper":{"title":"Intrinsic Flat Convergence of Covering Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Christina Sormani, Zahra Sinaei","submitted_at":"2014-09-24T22:47:47Z","abstract_excerpt":"We examine the limits of covering spaces and the covering spectra of oriented Riemannian manifolds, $M_j$, which converge to a nonzero integral current space, $M_\\infty$, in the intrinsic flat sense. We provide examples demonstrating that the covering spaces and covering spectra need not converge in this setting. In fact we provide a sequence of simply connected $M_j$ diffeomorphic to $\\mathbb{S}^4$ that converge in the intrinsic flat sense to a torus $\\mathbb{S}^1\\times\\mathbb{S}^3$. Nevertheless, we prove that if the $\\delta$-covers, $\\tilde{M}_j^\\delta$, have finite order $N$, then a subseq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7118","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":""},"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"}