In mathematics, especially in the area of algebraic topology known as stable homotopy theory, the Adams filtration and the Adams–Novikov filtration allow a stable homotopy group to be understood as built from layers, the nth layer containing just those maps which require at most n auxiliary spaces in order to be a composition of homologically trivial maps.
These filtrations, named after Frank Adams and Sergei Novikov, are of particular interest because the Adams (–Novikov) spectral sequence converges to them.
[1][2] The group of stable homotopy classes
between two spectra X and Y can be given a filtration by saying that a map
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.