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  3. Equivariant Stable Homotopy Theory and the Kervaire Invariant Problem
  • Cited by 3
Publisher:
Cambridge University Press
Online publication date:
June 2021
Print publication year:
2021
Online ISBN:
9781108917278
DOI:
https://doi.org/10.1017/9781108917278
Subjects:
Mathematics (general), Mathematics, Geometry and Topology
Series:
New Mathematical Monographs (40)
Information

Book 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.

Awards

Winner, 2022 PROSE Award for Mathematics

Reviews

‘… the book succeeds in simultaneously being readable as well as presenting a complex result, in providing tools without being lost in details, and in showing an exciting journey from classical to (at the time of this review) modern stable homotopy theory. Thus, we can expect that it will find a home on many topologists‘ bookshelves.’

Constanze Roitzheim Source: zbMATH

'The purpose of the book under review is to give an expanded and systematic development of the part of equivariant stable homotopy theory required by readers wishing to understand the proof of the Kervaire Invariant Theorem. The book fully achieves this design aim. The book ends with a 130-page summary of the proof of the theorem, and having this as a target shapes the entire narrative.'

J. P. C. Greenlees Source: MathSciNet

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