Cellular Spaces, Null Spaces and Homotopy Localization
Farjoun, Emmanuel Dror.
Cellular Spaces, Null Spaces and Homotopy Localization [electronic resource] / by Emmanuel Dror Farjoun. - XIV, 206 p. online resource. - Lecture Notes in Mathematics, 1622 0075-8434 ; . - Lecture Notes in Mathematics, 1622 .
Coaugmented homotopy idempotent localization functors -- Augmented homotopy idempotent functors -- Commutation rules for ?, Lf and CWA, preservation of fibrations and cofibrations -- Dold-Thom symmetric products and other colimits -- General theory of fibrations, GEM error terms -- Homological localization nearly preserves fibrations -- Classification of nullity and cellular types of finite p-torsion suspension spaces -- v 1-periodic spaces and K-theory -- Cellular inequalities.
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.
9783540484493
10.1007/BFb0094429 doi
Algebraic topology.
Topology.
Mathematics.
Algebraic Topology.
Topology.
Mathematics, general.
QA612-612.8
514.2
Cellular Spaces, Null Spaces and Homotopy Localization [electronic resource] / by Emmanuel Dror Farjoun. - XIV, 206 p. online resource. - Lecture Notes in Mathematics, 1622 0075-8434 ; . - Lecture Notes in Mathematics, 1622 .
Coaugmented homotopy idempotent localization functors -- Augmented homotopy idempotent functors -- Commutation rules for ?, Lf and CWA, preservation of fibrations and cofibrations -- Dold-Thom symmetric products and other colimits -- General theory of fibrations, GEM error terms -- Homological localization nearly preserves fibrations -- Classification of nullity and cellular types of finite p-torsion suspension spaces -- v 1-periodic spaces and K-theory -- Cellular inequalities.
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.
9783540484493
10.1007/BFb0094429 doi
Algebraic topology.
Topology.
Mathematics.
Algebraic Topology.
Topology.
Mathematics, general.
QA612-612.8
514.2