The 2-components of the 31-stem homotopy groups of the 9 and 10-spheres

TL;DR

This paper determines the previously incomplete 2-primary components of the 31-stem homotopy groups of spheres using Toda's composition method, advancing the understanding of sphere homotopy groups.

Contribution

It provides complete structures of the 2-primary components of the 31-stem homotopy groups, resolving earlier uncertainties in the field.

Findings

Complete structures of the 2-primary components of the 31-stem homotopy groups

Application of Toda's composition method to sphere homotopy groups

Resolution of previously incomplete group structures

Abstract

Group structures of the 2-primary components of the 31-stem homotopy groups of spheres were studied by Oda in 1979. There are, however, two incompletely determined groups. In this paper, our investigation with Toda's composition method gives structures of them.