A conjecture on homotopy groups of spheres, details on the algebra of higher cohomology operations

TL;DR

This paper explores a conjecture about the algebraic structure of higher cohomology operations, linking it to homotopy groups of spheres and the Adams spectral sequence, advancing understanding in algebraic topology.

Contribution

It proposes a new conjecture on the algebra of higher cohomology operations and discusses its implications for homotopy groups of spheres and spectral sequences.

Findings

Conjecture relates higher cohomology operations to homotopy groups.

Connections established with the Adams spectral sequence.

Provides detailed discussion on the algebraic structures involved.

Abstract

The theory of secondary chomology operations leads to a conjecture concerning the algebra of higher cohomology operations in general. This conjecture is discussed here in detail and its connection with homotopy groups of spheres and the Adams spectral sequence is described.