Extending Adams' theorem from singly generated to periodic cohomology

TL;DR

This paper discusses a conjecture to extend Adams' theorem on singly generated cohomology rings to periodic cohomology, providing a proof for a specific case, thereby advancing the understanding of cohomology operations.

Contribution

The paper proposes a conjecture extending Adams' theorem and proves it in a particular case, contributing to the theory of cohomology operations.

Findings

Proposed a conjecture extending Adams' theorem.

Proved the conjecture in a special case.

Enhanced understanding of periodic cohomology.

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.