On the First, the Second and the Third Stems of the Stable Homotopy Groups of Spheres

TL;DR

This paper explores the initial three stems of the stable homotopy groups of spheres using Puppe sequences, Thom complexes, K-Theory, and Adams operations, avoiding spectral sequences and Steenrod operations.

Contribution

It introduces a novel approach to describe the first three stems of stable homotopy groups without relying on spectral sequences or Steenrod operations.

Findings

Describes the first stem using Puppe sequences and K-Theory.

Provides insights into the second and third stems with the same methods.

Offers a new perspective on stable homotopy groups of spheres.

Abstract

We describe the first stem of the stable homotopy groups of spheres by using some Puppe sequences, Thom complexes, K-Theory and Adams operations following the ideas of J. Frank Adams. We also touch upon the second and the third stems in this perspective. Neither spectral squences nor Steenrod operations are used.