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# 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

#### 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.