Connected covers and Neisendorfer's localization theorem
Fundamenta Mathematicae, Tome 152 (1997) no. 3, pp. 211-230
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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{10_4064_fm_152_3_211_230,
author = {C. A. McGibbon and J. M. M{\o}ller},
title = {Connected covers and {Neisendorfer's} localization theorem},
journal = {Fundamenta Mathematicae},
pages = {211--230},
publisher = {mathdoc},
volume = {152},
number = {3},
year = {1997},
doi = {10.4064/fm-152-3-211-230},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm-152-3-211-230/}
}
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C. A. McGibbon; J. M. Møller. Connected covers and Neisendorfer's localization theorem. Fundamenta Mathematicae, Tome 152 (1997) no. 3, pp. 211-230. doi: 10.4064/fm-152-3-211-230
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