Current Developments in Mathematics

Volume 2010

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

Pages: 1 – 44

DOI: http://dx.doi.org/10.4310/CDM.2010.v2010.n1.a1

Authors

Michael A. Hill (Department of Mathematics, University of Virginia)

Michael J. Hopkins (Department of Mathematics, Harvard University)

Douglas C. Ravenel (Department of Mathematics, University of Rochester, New York)

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.

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