On the nonexistence of elements of Kervaire invariant one

Michael A. Hill, Michael J. Hopkins, Douglas C. Ravenel

Type: Article

Publication Date: 2016-05-26

Citations: 355

DOI: https://doi.org/10.4007/annals.2016.184.1.1

Abstract

We show that the Kervaire invariant one elements θj ∈ π2j+1−2S 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.

Locations

arXiv (Cornell University) - View - PDF
Annals of Mathematics - View

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