# nLab stem

Contents

### Context

#### Stable Homotopy theory

stable homotopy theory

Introduction

# Contents

## Definition

For $k \in \mathbb{Z}$, the $k$-stem of the homotopy groups of spheres is the collection of homotopy groups of the form $\pi_{n+k}(S^n)$ for all $n \in \mathbb{N}$, together with the suspension maps between them.

For $n \gt k + 1$ these groups stabilize (“stable stems”) and yield the stable homotopy groups of spheres.

## References

The “stem”-terminology is due to:

(which otherwise introduced the Freudenthal suspension theorem).

For more see the references at homotopy groups of spheres, such as

Last revised on March 1, 2021 at 13:28:17. See the history of this page for a list of all contributions to it.