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Parametrized Homotopy Theory

J. P. May and J. Sigurdsson
Publisher: 
American Mathematical Society
Publication Date: 
2006
Number of Pages: 
441
Format: 
Hardcover
Series: 
Mathematical Surveys and Monographs 132
Price: 
99.00
ISBN: 
0821839225
Category: 
Monograph
We do not plan to review this book.
  • 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

Dummy View - NOT TO BE DELETED