Spectral Sequences in Algebraic Topology

Only about 100 pages of the projected book are available. You can download PDF files by clicking on the links below.

Table of Contents (very tentative):

Chapter 1. The Serre Spectral Sequence
1. The Homology Spectral Sequence
Exact couples. The main theorem. Serre classes.
2. The Cohomology Spectral Sequence
Multiplicative structure. Rational homotopy groups. Localization of spaces. The EHP Sequence.
3. Eilenberg-MacLane Spaces
Mod 2 cohomology. Application to homotopy groups of spheres.
Chapter 2. The Adams Spectral Sequence
1. Spectra
2. Constructing the Spectral Sequence
3. Applications (Homotopy Groups of Spheres, Cobordism, The BP Spectrum, ...)
Chapter 3. Eilenberg-Moore Spectral Sequences
1. The Homology Spectral Sequence
2. The Cohomology Spectral Sequence
Additional topics that it would be nice to include:
A. The Bockstein Spectral Sequence
B. The Mayer-Vietoris Spectral Sequence
C. The EHP Spectral Sequence
D. More on Localization
E. Bott Periodicity (the algebraic topology proof)