Curtis’s conjecture

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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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The paper states

Theorem 1.1

In The Stable Hurewicz Image of the Sphere at Two, 25 September 2026

Possible match to OpenAI’s description, selected from the papers’ main statements because it shares the most wording. No review confirming the selection is recorded.

The other possible matches are Corollary 1.2 (Eccles’s conjecture for spheres) in the same paper () and Corollary 1.3 (Finite positive stable Hurewicz image) in the same paper ().

The image of \bigoplus_{d>0}h_d is spanned over \F_2 by the Hurewicz images of the Hopf-invariant-one classes \eta,\nu,\sigma, in degrees 1,3,7, and the Kervaire-invariant-one classes \theta_j, in degrees 2^{j+1}-2, j\ge1, whenever they exist. In particular, Curtis’s conjecture is true in all positive degrees.

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Papers

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The Stable Hurewicz Image of the Sphere at Two

25 September 2026, current edition.

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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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33 references in The Stable Hurewicz Image of the Sphere at Two

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