Equivariant stable homotopy theory and the Kervaire invariant problem

Author(s)

• Hill, Michael A. (Michael Anthony)
• Hopkins, Michael J.
• Ravenel, Douglas C.

Bibliographic Information

Equivariant stable homotopy theory and the Kervaire invariant problem

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

（New mathematical monographs, 40）

Cambridge University Press, 2021

• hbk.

Note

Includes bibliographical references and index

Description and Table of Contents

Description

The long-standing Kervaire invariant problem in homotopy theory arose from geometric and differential topology in the 1960s and was quickly recognised as one of the most important problems in the field. In 2009 the authors of this book announced a solution to the problem, which was published to wide acclaim in a landmark Annals of Mathematics paper. The proof is long and involved, using many sophisticated tools of modern (equivariant) stable homotopy theory that are unfamiliar to non-experts. This book presents the proof together with a full development of all the background material to make it accessible to a graduate student with an elementary algebraic topology knowledge. There are explicit examples of constructions used in solving the problem. Also featuring a motivating history of the problem and numerous conceptual and expository improvements on the proof, this is the definitive account of the resolution of the Kervaire invariant problem.

Table of Contents

• 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.

by "Nielsen BookData"

• NCID: BC0776344X
• ISBN:
  • 9781108831444
• Country Code: uk
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Cambridge
• Pages/Volumes: ix, 870 p.
• Size: 25 cm
• Classification:
  • DC23 : 514.24
• Subject Headings:
  • LCSH : Homotopy theory
  • LCSH : Invariants
• Parent Bibliography ID:
  • BA65869793