On the non-existence of elements of Kervaire invariant one
Algebraic Topology
2015-05-26 v4 Geometric Topology
Abstract
We show that Kervaire invariant one elements in the homotopy groups of spheres exist only in dimensions at most 126. 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. With the exception of dimension 126 this resolves a longstanding problem in algebraic topology.
Keywords
Cite
@article{arxiv.0908.3724,
title = {On the non-existence of elements of Kervaire invariant one},
author = {Michael A. Hill and Michael J. Hopkins and Douglas C. Ravenel},
journal= {arXiv preprint arXiv:0908.3724},
year = {2015}
}
Comments
Revised with some typos corrected, references and clarifying minro comments added.. 221 pages