group cohomology, nonabelian group cohomology, Lie group cohomology
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
This page collects links related to
Stable homotopy and generalized homology
Chicago Lectures in Mathematics, 1974
The University of Chicago Press 1974
on stable homotopy theory and generalised homology theory, with emphasis on complex cobordism theory, complex oriented cohomology theory, and the Adams spectral sequence/Adams-Novikov spectral sequence (today: “chromatic homotopy theory”).
Consists of three lectures, each meant to be readable on their own, and there is overlap in topics. It’s part III that begins with an actual introduction to stable homotopy theory, and so the beginner might prefer to start reading with Part III. Also notice that on p. 87 it says that the material there in part II is to be regarded as superseding part I.
A very detailed and readable account based on these lectures is
The big story emerging here was later further developed in
Mike Hopkins, Complex oriented cohomology theories and the language of stacks, 1999
Doug Ravenel, Complex cobordism and stable homotopy groups of spheres, 1986/2003
This is about understanding the absolute base space Spec(S) by covering it with Spec(MU). See at Adams spectral sequences – As derived descent.
generalized Chern classes
universal complex orientation on MU (Lemma 4.6, example 4.7)
There is much to love in his book, but not in the foundational part on CW spectra. (Peter May, MO comment)
What Adams tries to construct here – the localization of the stable homotopy category at the class of $E$-equivalences – was later constructed by (Bousfield 79). See at Bousfield localization of spectra.
Last revised on January 25, 2021 at 10:42:37. See the history of this page for a list of all contributions to it.