Connection To The Adams Spectral Sequence and The Homotopy Groups of Spheres
The cohomology of the Steenrod algebra is the E2 term for the (p-local) Adams spectral sequence, whose abutment is the p-component of the stable homotopy groups of spheres. More specifically, the E2 term of this spectral sequence may be identified as
This is what is meant by the aphorism "the cohomology of the Steenrod algebra is an approximation to the stable homotopy groups of spheres."
Read more about this topic: Steenrod Algebra
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