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.

- 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)

- 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.

- 1. Spectra
- 2. Constructing the Spectral Sequence
- 3. Applications (Homotopy Groups of Spheres, Cobordism, The BP Spectrum, ...)

- 1. The Homology Spectral Sequence
- 2. The Cohomology Spectral Sequence

- 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)