Name: Equivariant Stable Homotopy Theory and the Kervaire Invariant Problem By Michael A. Hill (University of California, Los Angeles)
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Equivariant Stable Homotopy Theory and the Kervaire Invariant Problem Summary

Equivariant Stable Homotopy Theory and the Kervaire Invariant Problem by Michael A. Hill (University of California, Los Angeles)

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.

About Michael A. Hill (University of California, Los Angeles)

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. Michael J. Hopkins is Professor at Harvard University. His research concentrates on algebraic topology. In 2001, he was awarded the Oswald Veblen Prize in Geometry from the AMS for his work in homotopy theory, followed by the NAS Award in Mathematics in 2012 and the Nemmers Prize in Mathematics in 2014. Douglas C. Ravenel is the Fayerweather Professor of Mathematics at the University of Rochester. He is the author of two influential previous books in homotopy theory and roughly 75 journal articles on stable homotopy theory and algebraic topology.

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.

Additional information

Sku

NPB9781108831444

ISBN 13

9781108831444

ISBN 10

1108831443

Title

Equivariant Stable Homotopy Theory and the Kervaire Invariant Problem by Michael A. Hill (University of California, Los Angeles)

Author

Michael A. Hill (University of California, Los Angeles)

Series

New Mathematical Monographs

Condition

New

Binding type

Hardback

Publisher

Cambridge University Press

Year published

2021-07-29

Number of pages

888

Prizes

N/A

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Equivariant Stable Homotopy Theory and the Kervaire Invariant Problem Michael A. Hill (University of California, Los Angeles)

Equivariant Stable Homotopy Theory and the Kervaire Invariant Problem by Michael A. Hill (University of California, Los Angeles)

Summary

Equivariant Stable Homotopy Theory and the Kervaire Invariant Problem Summary

Equivariant Stable Homotopy Theory and the Kervaire Invariant Problem by Michael A. Hill (University of California, Los Angeles)

About Michael A. Hill (University of California, Los Angeles)

Table of Contents

Additional information

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