Journal
ANNALS OF MATHEMATICS
Volume 184, Issue 1, Pages 1-262Publisher
Princeton Univ, Dept Mathematics
DOI: 10.4007/annals.2016.184.1.1
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Funding
- NSF [DMS-0905160, DMS-1307896, DMS-0906194, DMS0901560]
- Sloan foundation
- DARPA [HR0011-10-1-0054-DOD35CAP, FA9550-07-1-0555]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1510417, 1307896] Funding Source: National Science Foundation
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We show that Kervaire invariant one elements theta(j) is an element of pi S-2j+1-2(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
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