A Guide for Computing Stable Homotopy Groups

TL;DR

This paper provides a comprehensive overview and practical guide to stable homotopy theory, including the stable homotopy category, Steenrod algebra, and Adams spectral sequence, with detailed examples for computational techniques.

Contribution

It offers a detailed, accessible guide to key tools and methods in stable homotopy theory, aiding researchers in computations and applications.

Findings

Detailed examples of stable homotopy computations

Clarification of the use of Adams spectral sequence

Insights into the structure of the stable homotopy category

Abstract

This paper contains an overview of background from stable homotopy theory used by Freed--Hopkins in their work on invertible extended topological field theories. We provide a working guide to the stable homotopy category, to the Steenrod algebra and to computations using the Adams spectral sequence. Many examples are worked out in detail to illustrate the techniques.