Journal Article

On the nonexistence of elements of Kervaire invariant one

M. A. Hill, M. J. Hopkins and D. C. Ravenel
Annals of Mathematics
SECOND SERIES, Vol. 184, No. 1 (July, 2016), pp. 1-262
https://www.jstor.org/stable/24735198
Page Count: 262
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On the nonexistence of elements of Kervaire invariant one
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Abstract

We show that the Kervaire invariant one elements $\theta _j \epsilon \pi _{2^{j+1}-2}S^0$ exist only for j ≤ 6. By Browder's Theorem, this means that smooth framed manifolds of Kervaire invariant one exist only in dimensions 2, 6, 14, 30, 62, and possibly 126. Except for dimension 126 this resolves a longstanding problem in algebraic topology.