Adams–Novikov spectral sequence


Homological algebra

homological algebra


nonabelian homological algebra


Basic definitions

Stable homotopy theory notions



diagram chasing

Homology theories


Stable Homotopy theory



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 /p\mathbb{Z}/p\mathbb{Z} bycomplex cobordism cohomology theory.

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.


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 original articles are

  • John Adams, On the structure and applications of the Steenrod algebra, Comm. Math. Helv. 32 (1958), 180–214.

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

Reviews include for instance

Revised on November 17, 2013 06:54:34 by Urs Schreiber (