On the nonexistence of elements of Kervaire invariant one

• 成果类型: Article
• 署名作者: Hill, M. A.; Hopkins, M. J.; Ravenel, D. C.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2016.184.1.1
• 发表日期: 2016
• 页码: 1-262
• 关键词: stable-homotopy; MANIFOLDS; ALGEBRAS; localization; CATEGORIES

摘要

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