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Splitting theorems for certain equivariant spectra


About this Title

L. Gaunce Lewis, Jr.

Publication: Memoirs of the American Mathematical Society
Publication Year 2000: Volume 144, Number 686
ISBNs: 978-0-8218-2046-9 (print); 978-1-4704-0277-8 (online)
DOI: http://dx.doi.org/10.1090/memo/0686
MathSciNet review: 1679450
MSC (1991): Primary 55P42; Secondary 55M35, 55N20, 55P91, 55R12

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Table of Contents


Chapters

  • Introduction
  • Notational conventions
  • Part 1. Geometrically split spectra
  • Section 1. The notion of a geometrically split -spectrum
  • Section 2. Geometrically split -spectra and -fixed-point spectra
  • Section 3. Geometrically split -spectra and II-fixed-point spectra
  • Section 4. Geometrically split spectra and finite groups
  • Section 5. The stable orbit category for an incomplete universe
  • Part 2. A toolkit for incomplete universes
  • Section 6. A vanishing theorem for fixed-point spectra
  • Section 7. Spanier-Whitehead duality and incomplete universes
  • Section 8. Change of group functors and families of subgroups
  • Section 9. Change of universe functors and families of subgroups
  • Section 10. The geometric fixed-point functor for incomplete universes
  • Section 11. The Wirthmüller isomorphism for incomplete universes
  • Section 12. An introduction to the Adams isomorphism for incomplete universes
  • Part 3. The longer proofs
  • Section 13. The proof of Proposition 3.10 and its consequences
  • Section 14. The proofs of the main splitting theorems
  • Section 15. The proof of the sharp Wirthmüller isomorphism theorem
  • Section 16. The proof of the Adams isomorphism theorem for incomplete universes
  • Section 17. The Adams transfer for incomplete universes