Only about 100 pages of the projected book are available. You can download
PDF files by clicking on the links below.
Chapter 1. An introduction to the Serre spectral
sequence, with a number of applications, mostly fairly standard. (67 pages,
last modified January 5, 2004)
Chapter 2. The Adams spectral sequence. What is
written so far is just the derivation of the basic spectral sequence (additive
structure only), after the necessary preliminaries on spectra, and illustrated
by a few computations of stable homotopy groups of spheres. The next thing
to be added will be the multiplicative structure, and then more applications.
(26 pages, last modified October 2, 2004.)
Chapter 3. Eilenberg-Moore spectral sequences. We
follow the geometric viewpoint due originally to Larry Smith and Luke Hodgkin,
rather than the more usual algebraic approach. At present all that is written
is the construction of the spectral sequences, without any applications. (12
pages, last modified August 8, 2003)
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)