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]

Definition

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The group of stable homotopy classes   between two spectra X and Y can be given a filtration by saying that a map   has filtration n if it can be written as a composite of maps

 

such that each individual 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.

References

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  1. ^ "mypapers". people.math.rochester.edu.
  2. ^ https://scholar.harvard.edu/files/rastern/files/adamsspectralsequence.pdf&ved=2ahUKEwjI-JDstJOEAxU4WEEAHThuAOI4ChAWegQIGxAB&usg=AOvVaw3_Ga18v-jBF18FS-U4KgPV