A topological space X is called an -bubble (n is a natural number, is Čech cohomology with integer coefficients) if its n-dimensional cohomology is nontrivial and the n-dimensional cohomology of every proper subspace is trivial. The main results of our paper are: (1) Any compact metrizable -bubble is locally connected; (2) There exists a 2-dimensional 2-acyclic compact metrizable ANR which does not contain any -bubbles; and (3) Every n-acyclic finite-dimensional -trivial metrizable compactum contains an -bubble.
@article{bwmeta1.element.bwnjournal-article-cmv75z1p39bwm,
author = {Umed Karimov and Du\v san Repov\v s},
title = {On $\check{H}^n$-bubbles in n-dimensional compacta},
journal = {Colloquium Mathematicae},
volume = {78},
year = {1998},
pages = {39-51},
zbl = {0887.55005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv75z1p39bwm}
}
Karimov, Umed; Repovš, Dušan. On $\check{H}^n$-bubbles in n-dimensional compacta. Colloquium Mathematicae, Tome 78 (1998) pp. 39-51. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv75z1p39bwm/
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