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
Famous quotes containing the word definition:
“... if, as women, we accept a philosophy of history that asserts that women are by definition assimilated into the male universal, that we can understand our past through a male lens—if we are unaware that women even have a history—we live our lives similarly unanchored, drifting in response to a veering wind of myth and bias.”
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“Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.”
—The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on “life” (based on wording in the First Edition, 1935)