Adams–Novikov spectral sequence


Homological algebra

homological algebra

(also nonabelian homological algebra)



Basic definitions

Stable homotopy theory notions



diagram chasing

Homology theories


Stable Homotopy theory



The Adams-Novikov spectral sequence is the EE-Adams spectral sequence, for E=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 EE any suitable E-infinity ring there is an Adams-Novikov-type spectral sequence involving EE-generalized cohomology/generalized homology. This fully general notion is often again just referred to as the EE-Adams spectral sequence. Accordingly, see there for more. For detailed introduction, see at Introduction to the Adams Spectral Sequence.


Adams Chart

Isaksen 14:

Relation to Brown-Peterson spectrum

The pp-component of the E 2E^2-term of the Adams-Novikov spectral sequence for the sphere spectrum, hence the one converging to the stable homotopy groups of spheres π *(𝕊)\pi_\ast(\mathbb{S}) is

Ext BP *(BP)(BP *,BP *), Ext_{BP_\ast(BP)}(BP_\ast, BP_\ast) \,,

where BPBP denotes the Brown-Peterson spectrum at prime pp.

recalled e.g. as Ravenel, theorem 1.4.2


The generalization of the Adams spectral sequence from E=E = HA to E=E = MU is due to

  • Sergei Novikov, The methods of algebraic topology from the viewpoint of cobordism theories, Izv. Akad. Nauk. SSSR. Ser. Mat. 31 (1967), 855–951 (Russian) (Novikov67)

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

The Adams chart of the ANSS for large order has been presented in

Revised on April 22, 2017 04:44:30 by Urs Schreiber (