Definition
The group of stable homotopy classes between two spectra X and Y can be given a filtration by saying that a map f: X → Y has filtration n if it can be written as a composite of maps X = X0 → X1 → ... → Xn = Y such that each individual map Xi → Xi+1 induces the zero map in some fixed homology theory E. If E is ordinary mod-p homology, this filtration is called the Adams filtration, otherwise the Adams-Novikov filtration.
Read more about this topic: Adams Filtration
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