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

Equivariant Stable Homotopy Theory and the Kervaire Invariant Problem

• Gebundenes Buch

Produktbeschreibung

"This unique book on modern topology looks well beyond traditional treatises, and explores spaces that may, but need not, be Hausdorff. This is essential for domain theory, the cornerstone of semantics of computer languages, where the Scott topology is almost never Hausdorff. For the first time in a single volume, this book covers basic material on metric and topological spaces, advanced material on complete partial orders, Stone duality, stable compactness, quasi-metric spaces, and much more. An early chapter on metric spaces serves as an invitation to the topic (continuity, limits, compactness, completeness) and forms a complete introductory course by itself"--

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.