Local cohomological properties of homogeneous ANR compacta

2014/11/13 by Valov, Vesko
#FOS: Mathematics #General Topology (math.GN) #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1411.3422

Abstract

In accordance with the Bing-Borsuk conjecture, we show that if X is an n-dimensional homogeneous metric ANR compactum and x∈ X, then there is a local basis at x consisting of connected open sets U such that the cohomological properties of U and bdU are similar to the properties of the closed ball \mathbb Bⁿ⊂\mathbb Rⁿ and its boundary \mathbb S^n-1. We also prove that a metric ANR compactum X of dimension n is dimensionally full-valued if and only if the group H_n(X,X∖ x) is not trivial for some x∈ X. This implies that every 3-dimensional homogeneous metric ANR compactum is dimensionally full-valued.

Related

• Local homological properties and cyclicity of homogeneous ANR compacta
• Local structure of homogeneous ANR-spaces
• Homological dimension and homogeneous ANR spaces
• Homogeneous locally compact spaces
• Separation of homogeneous connected locally compact spaces