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Homotopy theory is an important sub-field of algebraic topology. It is mainly concerned with the properties and structures of spaces which are invariant under homotopy. Chief among these are the homotopy groups of spaces, specifically those of spheres. Homotopy theory includes a broad set of ideas and techniques, such as cohomology theories, spectra and stable homotopy theory, model categories, spectral sequences, and classifying spaces.
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Chromatic filtration on stable homotopy
Chapter 5 of Ravenel's green book starts with the sentence “[The chromatic spectral sequence] is a mechanism for organizing the Adams-Novikov $E_2$ term and ultimately $\pi_*(S^0)$ itself." My referen …