Cellular Spaces, Null Spaces and Homotopy Localization

Emmanuel Dror Farjoun (auth.)3540606041, 9783540606048

In 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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Table of contents :
Coaugmented homotopy idempotent localization functors….Pages 1-38
Augmented homotopy idempotent functors….Pages 39-58
Commutation rules for Ω, L f and CW A , preservation of fibrations and cofibrations….Pages 59-78
Dold-Thom symmetric products and other colimits….Pages 79-99
General theory of fibrations, GEM error terms….Pages 100-126
Homological localization nearly preserves fibrations….Pages 127-134
Classification of nullity and cellular types of finite p -torsion suspension spaces….Pages 135-143
v 1 -periodic spaces and K -theory….Pages 144-154
Cellular inequalities….Pages 155-175