nLab Stable homotopy and generalised homology

Contents

Context

Cohomology

• Stable homotopy and generalized homology,

Chicago Lectures in mathematics, 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

This is about understanding the absolute base space Spec(S) by covering it with Spec(MU). See at Adams spectral sequences – As derived descent.

Contents

Part I

3. Homology

• Novikov operations?

Part III

3. Elementary properties of the category of CW-spectra

There is much to love in his book, but not in the foundational part on CW spectra. (Peter May, MO comment)

14. A category of fractions

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.