Parametrized homotopy theory /
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| Author / Creator: | May, J. Peter. |
|---|---|
| Imprint: | Providence, R.I. : American Mathematical Society, c2006. |
| Description: | ix, 441 p. : ill. ; 27 cm. |
| Language: | English |
| Series: | Mathematical surveys and monographs, 0076-5376 ; v. 132 Mathematical surveys and monographs ; no. 132. |
| Subject: | |
| Format: | E-Resource Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/6202809 |
Table of Contents:
- Prologue Point-set topology, change functors, and proper actions
- Introduction to Part I
- The point-set topology of parametrized spaces
- Change functors and compatibility relations
- Proper actions, equivariant bundles and fibrations
- Model categories and parametrized spaces
- Introduction to Part II
- Topologically bicomplete model categories
- Well-grounded topological model categories
- The $qf$-model structure on $\mathcal{{K}}_B$
- Equivariant $qf$-type model structures
- Ex-fibrations and ex-quasifibrations
- The equivalence between Ho$G\mathcal{{K}}_B$ and $hG\mathcal{{W}}_B$
- Parametrized equivariant stable homotopy theory
- Introduction to Part III
- Enriched categories and $G$-categories
- The category of orthogonal $G$-spectra over $B$
- Model structures for parametrized $G$-spectra
- Adjunctions and compatibility relations
- Module categories, change of universe, and change of groups
- Parametrized duality theory
- Introduction to Part IV
- Fiberwise duality and transfer maps
- Closed symmetric bicategories
- The closed symmetric bicategory of parametrized spectra
- Costenoble-Waner duality
- Fiberwise Costenoble-Waner duality
- Homology and cohomology, Thom spectra, and addenda
- Introduction to Part V
- Parametrized homology and cohomology theories
- Equivariant parametrized homology and cohomology
- Twisted theories and spectral sequences
- Parametrized FSP's and generalized
- Thom spectra Epilogue: Cellular philosophy and alternative approaches
- Bibliography Index
- Index of notation