Lecture time and place: MWF 2:30, CHL 105
Instructor: John Palmieri
Padelford C-538, 543-1785
E-mail: palmieri@math.washington.edu
Office hours: by appointment
Web: http://www.math.washington.edu/~palmieri/Math583/

Text: Some of the time, I'll use A User's Guide to Spectral Sequences, 2nd edition, by John McCleary. See also errata on McCleary's web page.

We'll be using original sources, as well, such as Leray's seminal papers [2], Serre's paper [5] on his spectral sequence, and Novikov's work [4] on the generalized Adams spectral sequence. Hopf [1] is another important paper.

Homework: There will be problem sets, roughly every two weeks. You may work with other people on the homework. If you find a solution in a book, please provide a reference.

Final exam: This course will have a final exam, Tuesday, June 11, 2:30-4:20, place TBA (probably CHL 105). Alternatively, you can prepare a final project for the course. This would include a written portion (5-10 pages) plus a class presentation; the ideal topic would be a spectral sequence that we aren't covering in the course. Talk to me if you're interested in this option, and we can hash out the details.

Grading:

• 35%: final exam or final project
• 65%: class participation and homework

Plan for the course: We'll start with basics of spectral sequences: the spectral sequence arising from a filtered complex, the spectral sequence arising from a double complex, and exact couples. We'll certainly discuss the Bockstein spectral sequence and the Serre spectral sequence. Other potential topics include the Eilenberg-Moore spectral sequence, the composite functor spectral sequence, and Boardman's work on convergence. I hope that at the end of the course, we'll study the Adams spectral sequence.

References

1. H. Hopf, Über die Topologie der Gruppenmannigfaltigkeiten und ihre Verallgemeinerungen, Ann. Math. 42 (1941), 22-52.
2. J. Leray, Sur la forme des espaces topologiques et sur les points fixes des représentations, Sur la position d'un ensemble fermé de points d'un espace topologique, Sur les équations et les transformations, J. Math. Pures Appl. 24 (1945), 95-167, 169-199, 201-248;
3. J. McCleary, A User's Guide to Spectral Sequences, 2nd edition. Cambridge University Press, Cambridge (2001).
4. S. P. Novikov, The methods of algebraic topology from the viewpoint of cobordism theory (in Russian), Izvestia Akad. Nauk SSSR Ser. Mat. 31 (1967), 855-951.
5. J.-P. Serre, Homologie singulière des espaces fibrés, Ann. Math. 54 (1951), 425-505