Local cohomological properties of homogeneous ANR compacta

• Autorzy: V. Valov
• Języki publikacji: EN

Abstrakty

EN

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

Kategorie tematyczne

• 55M15: Absolute neighborhood retracts
• 55M10: Dimension theory
• 54C55: Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties)
• 54F45: Dimension theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2016
• Tom: 233
• Numer: 3
• Strony: 257-270

Daty

wydano

2016

Twórcy

autor

V. Valov

• Department of Computer Science and Mathematics, Nipissing University, 100 College Drive, P.O. Box 5002, North Bay, ON, P1B 8L7, Canada

Identyfikatory

DOI

10.4064/fm93-12-2015