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Local cohomological properties of homogeneous ANR compacta

Tom 233 / 2016

V. Valov Fundamenta Mathematicae 233 (2016), 257-270 MSC: Primary 55M10, 55M15; Secondary 54F45, 54C55. DOI: 10.4064/fm93-12-2015 Opublikowany online: 16 December 2015

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.

Autorzy

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

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