Michael A. Hill, Michael J. Hopkins, Douglas C. Ravenel

Equivariant Stable Homotopy Theory and the Kervaire Invariant Problem

• Gebundenes Buch

Produktbeschreibung

This is the definitive account of the resolution of the Kervaire invariant problem, a major milestone in algebraic topology. It develops all the machinery that is needed for the proof, and details many explicit constructions and computations performed along the way, making it suitable for graduate students as well as experts in homotopy theory.

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Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 882
• Erscheinungstermin: 29. Juli 2021
• Englisch
• Abmessung: 250mm x 175mm x 51mm
• Gewicht: 1670g
• ISBN-13: 9781108831444
• ISBN-10: 1108831443
• Artikelnr.: 60403549

Autorenporträt

Michael A. Hill is Professor at the University of California, Los Angeles. He is the author of several papers on algebraic topology and is an editor for journals including Mathematische Zeitschrift and Transactions of the American Mathematical Society.

Inhaltsangabe

1. Introduction
Part I. The Categorical Tool Box: 2. Some Categorical Tools
3. Enriched Category Theory
4. Quillen's Theory of Model Categories
5. Model Category Theory Since Quillen
6. Bousfield Localization
Part II. Setting Up Equivariant Stable Homotopy Theory: 7. Spectra and Stable Homotopy Theory
8. Equivariant Homotopy Theory
9. Orthogonal G-spectra
10. Multiplicative Properties of G-spectra
Part III. Proving the Kervaire Invariant Theorem: 11. The Slice Filtration and Slice Spectral Sequence
12. The Construction and Properties of $MU_{\R}$
13. The Proofs of the Gap, Periodicity and Detection Theorems
References
Table of Notation
Index.