(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 refine the classical Adams spectral sequence by replacing ordinary cohomology with coefficients in Fp by complex cobordism cohomology theory MU. This makes the Adams-Novikov spectral sequence converge to the full homotopy groups of connective spectra, hence in particular to the full stable homotopy groups of spheres (Novikov 67, Theorems 3.1, 3.3, reviewed as Ravenel 78, Thm. 3.1).
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
Further early development of this Adams-Novikov spectral sequence:
Review:
Douglas Ravenel, A Novice’s guide to the Adams-Novikov spectral sequence, in: Michael Barratt, Mark Mahowald (eds.) Geometric Applications of Homotopy Theory II. Lecture Notes in Mathematics, vol 658, Springer 1978 (doi:10.1007/BFb0068728, pdf)
Douglas 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 February 8, 2021 at 08:53:20. See the history of this page for a list of all contributions to it.