A User's Guide to Spectral Sequences

John McCleary is Professor of Mathematics at Vassar College on the Elizabeth Stillman Williams Chair. His research interests lie at the boundary between geometry and topology, especially where algebraic topology plays a role. His papers on topology have appeared in Inventiones Mathematicae, the American Journal of Mathematics and other journals, and he has written expository papers that have appeared in American Mathematical Monthly. He is also interested in the history of mathematics, especially the history of geometry in the nineteenth century and of topology in the twentieth century. He is the author of Geometry from a Differentiable Viewpoint and A First Course in Topology: Continuity and Dimension and he has edited proceedings in topology and in history, as well as a volume of the collected works of John Milnor. He has been a visitor to the mathematics institutes in Goettingen, Strasbourg and Cambridge, and to MSRI in Berkeley.

Part I. Algebra: 1. An informal introduction; 2. What is a spectral sequence?; 3. Tools and examples; Part II. Topology: 4. Topological background; 5. The Leray–Serre spectral sequence I; 6. The Leray–Serre spectral sequence II; 7. The Eilenberg–Moore spectral sequence I; 8. The Eilenberg–Moore spectral sequence II; 9. The Adams spectral sequence; 10. The Bockstein spectral sequence; Part III. Sins of Omission: 11. Spectral sequences in algebra, algebraic geometry and algebraic K-theory; 12. More spectral sequences in topology.