Connected covers and Neisendorfer's localization theorem

C. McGibbon; J. Møller

Fundamenta Mathematicae (1997)

  • Volume: 152, Issue: 3, page 211-230
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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McGibbon, C., and Møller, J.. "Connected covers and Neisendorfer's localization theorem." Fundamenta Mathematicae 152.3 (1997): 211-230. <http://eudml.org/doc/212208>.

@article{McGibbon1997,
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.},
author = {McGibbon, C., Møller, J.},
journal = {Fundamenta Mathematicae},
keywords = {-connected cover; Mislin genus; phantom maps; Lyusternik-Shnirel'man category},
language = {eng},
number = {3},
pages = {211-230},
title = {Connected covers and Neisendorfer's localization theorem},
url = {http://eudml.org/doc/212208},
volume = {152},
year = {1997},
}

TY - JOUR
AU - McGibbon, C.
AU - Møller, J.
TI - Connected covers and Neisendorfer's localization theorem
JO - Fundamenta Mathematicae
PY - 1997
VL - 152
IS - 3
SP - 211
EP - 230
AB - 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.
LA - eng
KW - -connected cover; Mislin genus; phantom maps; Lyusternik-Shnirel'man category
UR - http://eudml.org/doc/212208
ER -

References

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