Homogeneous ANR-spaces and Alexandroff manifolds

2014/03/18 by Vesko Valov, V. Valov, Valov, V.
Mathematics · #55M10 #55M15 #FOS: Mathematics #General Topology (math.GN) #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #math.GN #math.GT #msc:55M10 #msc:55M15

paper · pdf · doi:10.48550/arxiv.1403.4347

10 pages

arxiv created 2014/03/18 · openalex publication_date 2014/03/18 · arxiv updated 2014/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We specify a result of Yokoi \citeyo by proving that if G is an abelian group and X is a homogeneous metric ANR compactum with dim_GX=n and \checkHⁿ(X;G)≠ 0, then X is an (n,G)-bubble. This implies that any such space X has the following properties: \checkH^n-1(A;G)≠ 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≤ n-2. We also prove that if X is a homogeneous metric continuum with \checkHⁿ(X;G)≠ 0, then \checkH^n-1(C;G)≠ 0 for any partition C of X such that dim_GC≤ n-1. The last provides a partial answer to a question of Kallipoliti and Papasoglu \citekp.

Related

• Alexandroff type manifolds and homology manifolds
• Alexandroff Manifolds and Homogeneous Continua
• Local structure of homogeneous ANR-spaces
• Homogeneous locally compact spaces
• Homological dimension and homogeneous ANR spaces