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Modern Classical Homotopy Theory

About this Title

Jeffrey Strom, Western Michigan University, Kalamazoo, MI

Publication: Graduate Studies in Mathematics
Publication Year: 2011; Volume 127
ISBNs: 978-0-8218-5286-6 (print); 978-1-4704-1188-6 (online)
DOI: https://doi.org/10.1090/gsm/127
MathSciNet review: MR2839990
MSC: Primary 55-01; Secondary 55-02, 55Pxx, 55Qxx, 55Uxx

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Table of Contents

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Front/Back Matter

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Part 1. The language of categories

• Chapter 1. Categories and functors
• Chapter 2. Limits and colimits

Part 2. Semi-formal homotopy theory

• Chapter 3. Categories of spaces
• Chapter 4. Homotopy
• Chapter 5. Cofibrations and fibrations
• Chapter 6. Homotopy limits and colimits
• Chapter 7. Homotopy pushout and pullback squares
• Chapter 8. Tools and techniques
• Chapter 9. Topics and examples
• Chapter 10. Model categories

Part 3. Four topological inputs

• Chapter 11. The concept of dimension in homotopy theory
• Chapter 12. Subdivision of disks
• Chapter 13. The local nature of fibrations
• Chapter 14. Pullbacks of cofibrations
• Chapter 15. Related topics

Part 4. Targets as domains, domains as targets

• Chapter 16. Constructions of spaces and maps
• Chapter 17. Understanding suspension
• Chapter 18. Comparing pushouts and pullbacks
• Chapter 19. Some computations in homotopy theory
• Chapter 20. Further topics

Part 5. Cohomology and homology

• Chapter 21. Cohomology
• Chapter 22. Homology
• Chapter 23. Cohomology operations
• Chapter 24. Chain complexes
• Chapter 25. Topics, problems and projects

Part 6. Cohomology, homology and fibrations

• Chapter 26. The Wang sequence
• Chapter 27. Cohomology of filtered spaces
• Chapter 28. The Serre filtration of a fibration
• Chapter 29. Application: Incompressibility
• Chapter 30. The spectral sequence of a filtered space
• Chapter 31. The Leray-Serre spectral sequence
• Chapter 32. Application: Bott periodicity
• Chapter 33. Using the Leray-Serre spectral sequence

Part 7. Vistas

• Chapter 34. Localization and completion
• Chapter 35. Exponents for homotopy groups
• Chapter 36. Classes of spaces
• Chapter 37. Miller’s theorem
• Appendix A. Some algebra