On the nonexistence of elements of Kervaire invariant one

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 reso...

Full description

Saved in:
Bibliographic Details
Published in:Annals of mathematics 2016-07, Vol.184 (1), p.1-262
Main Authors: Hill, M. A., Hopkins, M. J., Ravenel, D. C.
Format: Article
Language:English
Subjects:
Adjoints
Algebra
Functors
Homotopy theory
Mathematical rings
Mathematical theorems
Monoids
Morphisms
Spectral index
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0003-486X
DOI:10.4007/annals.2016.184.1.1