## Cellular Spaces, Null Spaces and Homotopy LocalizationIn this monograph we give an exposition of some recent development in homotopy theory. It relates to advances in periodicity in homotopy localization and in cellular spaces. The notion of homotopy localization is treated quite generally and encompasses all the known idempotent homotopy functors. It is applied to K-theory localizations, to Morava-theories, to Hopkins-Smith theory of types. The method of homotopy colimits is used heavily. It is written with an advanced graduate student in topology and research homotopy theorist in mind. |

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### Contents

II | 1 |

III | 6 |

IV | 17 |

V | 23 |

VI | 26 |

VII | 28 |

VIII | 35 |

IX | 37 |

XXVII | 104 |

XXVIII | 112 |

XXIX | 116 |

XXX | 120 |

XXXI | 122 |

XXXII | 127 |

XXXIII | 128 |

XXXIV | 132 |

### Other editions - View all

Cellular Spaces, Null Spaces and Homotopy Localization Emmanuel D. Farjoun No preview available - 1995 |

Cellular Spaces, Null Spaces and Homotopy Localization Emmanuel D. Farjoun No preview available - 2014 |

### Common terms and phrases

1-connected A-cellular spaces A-equivalence abelian group acyclic spaces Appendix HL assume assumption base point base space Bousfield cellular Chapter claim classifying space closed class coaugmentation cofibration colim components connected space consider contractible COROLLARY CW-complexes CWAX define denote dimension direct limit Eilenberg-Mac Lane spaces error term example F-space fact factors fibration sequence fibre map fibrewise localization finite follows free diagram function complexes G-space GEM space given homological localization homology theory homotopy coend homotopy equivalence homotopy fibre homotopy groups homotopy inverse homotopy pushout homotopy type idempotent induced map infinite loop space lemma localization functor localization with respect map g mod-p natural map Notice null homotopic orbit oriented polyGEM p-torsion pointed diagram pointed homotopy colimit pointed spaces PROPOSITION pullback pushout retract simplicial complex simplicial sets simplicial space small category SPkX suspension symmetric product taking homotopy telescope theorem topological total space unpointed W-null weak equivalence Z/pZ