{"paper":{"title":"On macroscopic dimension of universal coverings of closed manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Alexander Dranishnikov","submitted_at":"2013-07-03T14:42:08Z","abstract_excerpt":"We give a homological characterization of $n$-manifolds whose universal covering $\\Wi M$ has Gromov's macroscopic dimension $\\dim_{mc}\\Wi M<n$. As the result we distinguish $\\dim_{mc}$ from the macroscopic dimension $\\dim_{MC}$ defined by the author \\cite{Dr}. We prove the inequality $\\dim_{mc}\\Wi M<\\dim_{MC}\\Wi M=n$ for every closed $n$-manifold $M$ whose fundamental group $\\pi$ is a geometrically finite amenable duality group with the cohomological dimension $cd(\\pi)> n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1029","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"}