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arXiv:0908.3724math.AT

On the non-existence of elements of Kervaire invariant one

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

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.

arXiv comments
Revised with some typos corrected, references and clarifying minro comments added.. 221 pages
Journal reference
DOI
Subjects
math.ATAlgebraic Topology math.GTGeometric Topology

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  1. Dimension 126 Contains Twisted Shapes, Mathematicians Prove 2 comments

    • > They’re all double the last dimension plus two, without skipping any in that sequence - but that offers no insight into why it wouldn’t hold for 254. Wikipedia at least gives a literature reference and concise explanation for the reason: >…

      aleph_minus_oneView on HNParent context

    • The proof that it stops instead of going on forever is here: https://arxiv.org/abs/0908.3724 It’s more than 200 pages of pretty technical mathematics, so I’m reasonably confident that there is no description a layperson might understand.

      robinhoustonView on HNParent context

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