Local cohomological properties of homogeneous ANR compacta

V. Valov

Fundamenta Mathematicae (2016)

  • Volume: 233, Issue: 3, page 257-270
  • ISSN: 0016-2736

Abstract

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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 ⁿ ⊂ ℝⁿ and its boundary 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.

How to cite

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V. Valov. "Local cohomological properties of homogeneous ANR compacta." Fundamenta Mathematicae 233.3 (2016): 257-270. <http://eudml.org/doc/283041>.

@article{V2016,
abstract = {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 ⁿ ⊂ ℝⁿ and its boundary $^\{n-1\}$. 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.},
author = {V. Valov},
journal = {Fundamenta Mathematicae},
keywords = {bing--borsuk conjecture for homogeneous compacta; cohomological carrier; cohomology groups; cohomological membrane; dimensionally full-valued compactum; homogeneous metric ANR compacta},
language = {eng},
number = {3},
pages = {257-270},
title = {Local cohomological properties of homogeneous ANR compacta},
url = {http://eudml.org/doc/283041},
volume = {233},
year = {2016},
}

TY - JOUR
AU - V. Valov
TI - Local cohomological properties of homogeneous ANR compacta
JO - Fundamenta Mathematicae
PY - 2016
VL - 233
IS - 3
SP - 257
EP - 270
AB - 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 ⁿ ⊂ ℝⁿ and its boundary $^{n-1}$. 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.
LA - eng
KW - bing--borsuk conjecture for homogeneous compacta; cohomological carrier; cohomology groups; cohomological membrane; dimensionally full-valued compactum; homogeneous metric ANR compacta
UR - http://eudml.org/doc/283041
ER -

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