Connected covers and Neisendorfer's localization theorem
Volume 152 / 1997
Fundamenta Mathematicae 152 (1997), 211-230 DOI: 10.4064/fm-152-3-211-230
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.