Current Developments in Mathematics

The Arf-Kervaire problem in algebraic topology: Sketch of the proof

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

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Abstract

We provide a sketch of the proof of the non-existence of Kervaire Invariant one manifolds using equivariant homotopy theory. A treatment of the statement and history of the problem can be found in “The Arf-Kervaire problem in algebraic topology: Introduction”. Our goal here is to introduce the reader to the techniques used to prove the result and to familiarize them with the kinds of computations needed.

Article information

Source
Current Developments in Mathematics, Volume 2010 (2011), 1-44.

Dates
First available in Project Euclid: 23 April 2012

Permanent link to this document
https://projecteuclid.org/euclid.cdm/1335196632

Mathematical Reviews number (MathSciNet)
MR2906370

Zentralblatt MATH identifier
1249.55005

Citation

Hill, Michael A.; Hopkins, Michael J.; Ravenel, Douglas C. The Arf-Kervaire problem in algebraic topology: Sketch of the proof. Current Developments in Mathematics 2010 (2011), 1--44. https://projecteuclid.org/euclid.cdm/1335196632


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