group cohomology, nonabelian group cohomology, Lie group cohomology
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
symmetric monoidal (∞,1)-category of spectra
The Landweber-Novikov theorem describes the structure of Hopf algebroid over a commutative base on the dual generalized Steenrod algebra of the complex cobordism cohomology theory spectrum MU.
By Quillen's theorem on MU we have $\pi_\bullet(MU) \simeq L$, the Lazard ring. Moreover the dual Steenrod algebra is
where on the right we have the polynomial ring on generators $b_i$ in degree $2i$.
Here $(L, L B)$ carries a natural structure of a Hopf algebroid over a commutative base (and apparently this example is what made Haynes Miller introduce Hopf algebroids in the first place). The Landweber-Novikov theorem asserts that this is the Hopf algebroid structure on the dual MU-Steenrod algebra
The analog for BP is the Adams-Quillen theorem.
The original articles are
Sergei Novikov, The metods of algebraic topology from the viewpoint of cobordism theories, Izv. Akad. Nauk. SSSR. Ser. Mat. 31 (1967), 855–951 (Russian).
Peter Landweber, Cobordism operations and Hopf algebras, Trans. Amer. Math. Soc. 129 (1967), 94–110.
Frank Adams, Part II.11 of Stable homotopy and generalised homology, 1974
The Hopf algebroid structure on $(L, L B)$ is reviewed in
The Landweber-Novikov theorem is reviewed in
Last revised on February 5, 2016 at 05:36:02. See the history of this page for a list of all contributions to it.