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A solution to the Arf-Kervaire invariant problem,
April, 2009.

Mike Hill, Mike Hopkins and I have recently solved the Arf-Kervaire invariant problem.

Our main theorem states that θj does not exist for j > 6. θj is a hypothetical element of order 2 in the stable homotopy groups of spheres in the (2j+1-2)-stem. It was previously known to exist for j < 6. The status of θ6 (in the 126-stem) remains open.

A collection of earlier and more recent papers on the problem

Talks since April, 2009
including 2013 NWU talk

Preprint of November 22, 2010
ON THE NON-EXISTENCE OF ELEMENTS OF KERVAIRE INVARIANT ONE  (158 pages)
arXiv link
Preprint of August 26, 2009
ON THE NON-EXISTENCE OF ELEMENTS OF KERVAIRE INVARIANT ONE  (99 pages)
arXiv link


            
Michel Kervaire (1927-2007)
       
Workshop on the Kervaire invariant
and stable homotopy theory

ICMS Edinburgh, 25-29 April, 2011.

MSRI Hot Topics Workshop: the Kervaire Invariant
Berkeley, California, October 25-29, 2010
Streaming videos are available at the link above.
Slides and notes from talks


Mike Hill, myself and Mike Hopkins
Photo taken by Bill Browder, February 11, 2010
Here are some relevant links.

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Created April 30, 2009; last modified March 27, 2013.