Our point of departure is J. Neisendorfer's localization theorem which reveals a subtle connection between some simply connected finite complexes and their connected covers. We show that even though the connected covers do not forget that they came from a finite complex their homotopy-theoretic properties are drastically different from those of finite complexes. For instance, connected covers of finite complexes may have uncountable genus or nontrivial SNT sets, their Lusternik-Schnirelmann category may be infinite, and they may serve as domains for nontrivial phantom maps.
@article{bwmeta1.element.bwnjournal-article-fmv152i3p211bwm,
author = {C. McGibbon and J. M\o ller},
title = {Connected covers and Neisendorfer's localization theorem},
journal = {Fundamenta Mathematicae},
volume = {154},
year = {1997},
pages = {211-230},
zbl = {0896.55014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv152i3p211bwm}
}
McGibbon, C.; Møller, J. Connected covers and Neisendorfer's localization theorem. Fundamenta Mathematicae, Tome 154 (1997) pp. 211-230. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv152i3p211bwm/
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