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Parametrized Homotopy Theory
About this Title
J. P. May, The University of Chicago, Chicago, IL and J. Sigurdsson, University of Sheffield, Sheffield, England
Publication: Mathematical Surveys and Monographs
Publication Year:
2006; Volume 132
ISBNs: 978-0-8218-3922-5 (print); 978-1-4704-1359-0 (online)
DOI: https://doi.org/10.1090/surv/132
MathSciNet review: MR2271789
MSC: Primary 55P42; Secondary 19L99, 55N20, 55N22, 55P91
Table of Contents
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Front/Back Matter
Chapters
- 1. The point-set topology of parametrized spaces
- 2. Change functors and compatibility relations
- 3. Proper actions, equivariant bundles and fibrations
- 4. Topologically bicomplete model categories
- 5. Well-grounded topological model categories
- 6. The $qf$-model structure on $\mathscr {K}_B$
- 7. Equivariant $qf$-type model structures
- 8. Ex-fibrations and ex-quasifibrations
- 9. The equivalence between Ho $G\mathscr {K}_B$ and $hG\mathscr {W}_B$
- 10. Enriched categories and $G$-categories
- 11. The category of orthogonal $G$-spectra over $B$
- 12. Model structures for parametrized $G$-spectra
- 13. Adjunctions and compatibility relations
- 14. Module categories, change of universe, and change of groups
- 15. Fiberwise duality and transfer maps
- 16. Closed symmetric bicategories
- 17. The closed symmetric bicategory of parametrized spectra
- 18. Costenoble-Waner duality
- 19. Fiberwise Costenoble-Waner duality
- 20. Parametrized homology and cohomology theories
- 21. Equivariant parametrized homology and cohomology
- 22. Twisted theories and spectral sequences
- 23. Parametrized FSP’s and generalized Thom spectra
- 24. Epilogue: cellular philosophy and alternative approaches