{"paper":{"title":"Homogeneous ANR-spaces and Alexandroff manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.GT","authors_text":"V. Valov","submitted_at":"2014-03-18T05:23:18Z","abstract_excerpt":"We specify a result of Yokoi \\cite{yo} by proving that if $G$ is an abelian group and $X$ is a homogeneous metric $ANR$ compactum with $\\dim_GX=n$ and $\\check{H}^n(X;G)\\neq 0$, then $X$ is an $(n,G)$-bubble. This implies that any such space $X$ has the following properties: $\\check{H}^{n-1}(A;G)\\neq 0$ for every closed separator $A$ of $X$, and $X$ is an Alexandroff manifold with respect to the class $D^{n-2}_G$ of all spaces of dimension $\\dim_G\\leq n-2$. We also prove that if $X$ is a homogeneous metric continuum with $\\check{H}^n(X;G)\\neq 0$, then $\\check{H}^{n-1}(C;G)\\neq 0$ for any partit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4347","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"}