Local cohomological properties of homogeneous ANR compacta
Tom 233 / 2016
Streszczenie
In accordance with the Bing–Borsuk conjecture, we show that if is an n-dimensional homogeneous metric ANR continuum and x\in X, then there is a local basis at x consisting of connected open sets U such that the cohomological properties of \overline U and {\rm bd}\,U are similar to the properties of the closed ball \mathbb B^n\subset \mathbb R^n 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\setminus x;\mathbb Z) is not trivial for some x\in X. This implies that every 3-dimensional homogeneous metric ANR compactum is dimensionally full-valued.