∑math20

Topology · Result 316

Curtis’s conjecture

1 paper

Proves Curtis’s conjecture: the positive-degree mod-two stable Hurewicz image of the sphere is spanned by the images of the Hopf-invariant-one classes η, ν, σ and the Kervaire-invariant-one classes that exist.

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▶Introduction: the problem and why it mattersin preparation
▶The presented solutionin preparation

Papers 1

First page of The Stable Hurewicz Image of the Sphere at Two

The Stable Hurewicz Image of the Sphere at Two

OpenAI · September 25, 2026

We prove Curtis's conjecture: in every positive degree, the mod-two stable Hurewicz image of the sphere is spanned by the images of η, ν, σ and the Kervaire-invariant-one classes that exist. Consequently, Eccles's conjecture holds for every sphere Sn with n > 0.

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@misc{OAI:The-Stable-Hurewicz-Image-of-the-Sphere-at-Two-September-25-2026,
  author = {{OpenAI}},
  title = {{The Stable Hurewicz Image of the Sphere at Two}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/The-Stable-Hurewicz-Image-of-the-Sphere-at-Two-September-25-2026/paper.pdf}{OAI:The-Stable-Hurewicz-Image-of-the-Sphere-at-Two-September-25-2026}},
  year = {2026}
}

Formal verification

No Lean formalization is listed for this result yet. The repository notes that unformalized results could have issues.