(also nonabelian homological algebra)
The Adams-Novikov spectral sequence is the $E$-Adams spectral sequence, for $E =$ MU.
More in detail, the Adams-Novikov spectral sequence is a class of spectral sequences which converge to and hence are used to compute homotopy groups of connective spectra, hence in particular the stable homotopy groups of spheres. It refines the Adams spectral sequence by replacing ordinary cohomology with coefficients in Fp by complex cobordism cohomology theory, i.e. with coefficients in MU.
More generally for $E$ any suitable E-infinity ring there is an Adams-Novikov-type spectral sequence involving $E$-generalized cohomology/generalized homology. This fully general notion is often again just referred to as the $E$-Adams spectral sequence. Accordingly, see there for more. For detailed introduction, see at Introduction to the Adams Spectral Sequence.
The $p$-component of the $E^2$-term of the Adams-Novikov spectral sequence for the sphere spectrum, hence the one converging to the stable homotopy groups of spheres $\pi_\ast(\mathbb{S})$ is
where $BP$ denotes the Brown-Peterson spectrum at prime $p$.
recalled e.g. as Ravenel, theorem 1.4.2
The generalization of the Adams spectral sequence from $E =$ HA to $E =$ MU is due to
While that article was still being translated to English, Frank Adams learned of and then lectured about this work in 1967 in Chicago. This lecture together with two later lectures in 1970 and in 1971 constitute the book
Reviews include
Doug Ravenel, Complex cobordism and stable homotopy groups of spheres, page 11 of chapter I An introduction to the homotopy groups of spheres (pdf)
Doug Ravenel, Complex cobordism and stable homotopy groups of spheres, chapter IV $B P$-Theory and the Adams-Novikov Spectral Sequence (pdf)
Stanley Kochman, sections 4.7 and 5.6 of Bordism, Stable Homotopy and Adams Spectral Sequences, AMS 1996
Jacob Lurie, Localizations and the Adams-Novikov Spectral Sequence (pdf)
The Adams chart of the ANSS for large order has been presented in
Last revised on March 12, 2019 at 19:38:35. See the history of this page for a list of all contributions to it.