On the nonexistence of elements of Kervaire invariant one

M. A. Hill; M. J. Hopkins; D. C. Ravenel

doi:10.4007/annals.2016.184.1.1

On the nonexistence of elements of Kervaire invariant one

M. A. Hill, M. J. Hopkins, D. C. Ravenel

Research output: Contribution to journal › Article › peer-review

174 Scopus citations

Abstract

We show that the Kervaire invariant one elements θ_j ∈ π_2j+1-2S⁰ 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.

Original language	English (US)
Pages (from-to)	1-262
Number of pages	262
Journal	Annals of Mathematics
Volume	184
Issue number	1
DOIs	https://doi.org/10.4007/annals.2016.184.1.1
State	Published - Jul 1 2016
Externally published	Yes

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© 2016 Department of Mathematics, Princeton University.

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AB - We show that the Kervaire invariant one elements θj ∈ π2j+1-2S0 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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On the nonexistence of elements of Kervaire invariant one

Abstract

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