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ArticleOriginal scientific text

Title

Connected covers and Neisendorfer's localization theorem

Authors 1, 2

Affiliations

  1. Mathematics Department, Wayne State University, Detroit, Michigan 48202, U.S.A.
  2. Matematisk Institut, Københavns Universitet, Universitetsparken 5, DK-2100 København Ø, Denmark

Abstract

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.

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Fundamenta Mathematicae
1997/152/3
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Pages:
211-230
Main language of publication
English
Received
1996-06-24
Accepted
1996-12-02
Published
1997
Exact and natural sciences