Extending Adams' theorem from singly generated to periodic cohomology

2024/12/20 by John R. Harper, Harper, John R., Lee Kennard +1 · 1 citation
Mathematics · #53C20 #55R45 #55S10 (Primary) 20F50 #55S20 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #K-Theory and Homology (math.KT) #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2412.16340

openalex publication_date 2024/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 1960, J.F. Adams introduced secondary cohomology operations that are defined on cohomology elements on which sufficiently many Steenrod algebra elements vanish. This led to his theorem on singly generated cohomology rings, which in turn led to his celebrated resolution of the Hopf invariant one problem. Here we advertise a conjecture that would extend Adams' result and prove it in a special case.

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• On Hopf's conjecture and positive second intermediate Ricci curvature

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