On the Last Kervaire Invariant Problem

2024/12/14 by Weinan Lin, Guozhen Wang, Lin, Weinan +3 · 3 voices · 4 citations
#math.AT #math.DG #math.GT

paper · pdf · doi:10.48550/arxiv.2412.10879

Abstract

We prove that the element h₆² is a permanent cycle in the Adams spectral sequence. As a result, we establish the existence of smooth framed manifolds with Kervaire invariant one in dimension 126, thereby resolving the final case of the Kervaire invariant problem. Combining this result with the theorems of Browder, Mahowald--Tangora, Barratt--Jones--Mahowald, and Hill--Hopkins--Ravenel, we conclude that smooth framed manifolds with Kervaire invariant one exist in and only in dimensions 2, 6, 14, 30, 62, and 126.

Cited by

• Periodicity and finite complexity in higher real K-theories
• Slice spectral sequences through synthetic spectra
• Graphs arising from the dual Steenrod algebra
• Manifold structures on highly connected Poincaré complexes

Discussions

• Kervaire invariant DONE! arxiv.org/abs/2412.10879 [bsky, 19 points, 1 comments]
• it’s out! complete closure to kervaire invariant one problem! arxiv.org/abs/2412.10879 [bsky, 12 points, 1 comments]
• This is written in a language I know, on a topic I, a layman, find interesting. I literally don't understand a word of it: arxiv.org/pdf/2412.10879 (this basically says that there are some weird shape [bsky, 0 points, 0 comments]

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