# 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: Primary 55P42; Secondary 55M35, 55N20, 55P91, 55R12

### Table of Contents

**Chapters**

- Introduction
- Notational conventions
- Part 1. Geometrically split spectra
- Section 1. The notion of a geometrically split $G$-spectrum
- Section 2. Geometrically split $G$-spectra and $G$-fixed-point spectra
- Section 3. Geometrically split $G$-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 $\Phi ^\Lambda $ 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