

Drawing by Carolyn Snaith published in 1982, Larger picture 
The Arf invariant Arf(q) of a quadratic form q is defined on the 2009 banknote shown above. Larger picture 
Michel Kervaire (19272007)  and stable homotopy theory ICMS Edinburgh, 2529 April, 2011. 
Berkeley, California, October 2529, 2010 Streaming videos are available at the link above. Slides and notes from talks 
As ideas for progress on a particular mathematics problem atrophy it can disappear. Accordingly I wrote this book to stem the tide of oblivion.
For a brief period overnight we were convinced that we had the method to make all the sought after framed manifolds  a feeling which must have been shared by many topologists working on this problem. All in all, the temporary high of believing that one had the construction was sufficient to maintain in me at least an enthusiastic spectator's interest in the problem.
In the light of the above conjecture and the failure over fifty years to construct framed manifolds of ArfKervaire invariant one this might turn out to be a book about things which do not exist. This [is] why the quotations which preface each chapter contain a preponderance of utterances from the pen of Lewis Carroll.
Victor Snaith and William Browder in 1981 
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