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Author:   Jeffrey Strom
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
ISBN:  

9781470471637

ISBN 10:   1470471639
Pages:   835
Publication Date:   30 January 2011
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

The language of categories: Categories and functors Limits and colimits Semi-formal homotopy theory: Categories of spaces Homotopy Cofibrations and fibrations Homotopy limits and colimits Homotopy pushout and pullback squares Tools and techniques Topics and examples Model categories Four topological inputs: The concept of dimension in homotopy theory Subdivision of disks The local nature of fibrations Pullbacks of cofibrations Related topics Targets as domains, domains as targets: Constructions of spaces and maps Understanding suspension Comparing pushouts and pullbacks Some computations in homotopy theory Further topics Cohomology and homology: Cohomology Homology Cohomology operations Chain complexes Topics, problems and projects Cohomology, homology and fibrations: The Wang sequence Cohomology of filtered spaces The Serre filtration of a fibration Application: Incompressibility The spectral sequence of a filtered space The Leray-Serre spectral sequence Application: Bott periodicity Using the Leray-Serre spectral sequence Vistas: Localization and completion Exponents for homotopy groups Classes of spaces Miller's theorem Some algebra References Index of notation Index

Reviews

Obviously the book was a labor of love for its author: this is visible on every page. The coverage of the material is, in a word, amazing, even to an outsider like me. The book is well-written, as I have already indicated, and Strom's problems first-and-foremost approach is bound to be a big pedagogical hit for those who can handle it, both in front of the class and in it. The book under review is a wonderful contribution indeed. - MAA Reviews

Obviously the book was a labor of love for its author: this is visible on every page. The coverage of the material is, in a word, amazing, even to an outsider like me. The book is well-written, as I have already indicated, and Strom's """"problems first-and-foremost"""" approach is bound to be a big pedagogical hit for those who can handle it, both in front of the class and in it. The book under review is a wonderful contribution indeed."""" - MAA Reviews

Author Information

Jeffrey Strom, Western Michigan University, Kalamazoo, MI.

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