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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

### Table of Contents

**Download chapters as PDF**

**Front/Back Matter**

**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. Millerâ€™s theorem
- Appendix A. Some algebra