Course material available:

• The April Fool's syllabus and the real syllabus.
• Homology handout (PDF format). If you don't know anything about homology and cohomology of spaces, you can find some information here.
• Fibrations handout (PDF format). Brief introduction to fibrations.
• Bockstein handout (PDF format). A brief description of an approach to the Bockstein spectral sequence, as I did it in class.

Homework:

Material covered:

Rough outline, reading:

• Week 1. Introduction, then look at filtered chain complexes. You might want to skim Chapter 1 of McCleary, and also Section 2.1. Filtered chain complexes appear in Section 2.2.
• Weeks 2 and 3. More on filtered chain complexes. Examples: the Bockstein spectral sequence and maybe cellular homology. Look at exact couples (2.2). Example: the Bockstein spectral sequence. Then look at double complexes (Section 2.4). Example: balancing Tor.
• Week 4. Spectral sequences of algebras (Section 2.3). Example: the Serre spectral sequence, cohomology of loop spaces (Chapter 5).
• Weeks 5 and 6. Group cohomology and the Lyndon-Hochschild-Serre spectral sequence (pp. 340-344).
• Weeks 7 and 8. Hopf algebra cohomology and the relevant spectral sequence. The Grothendieck spectral sequence
• Weeks 9 and 10. Triangulated categories and the Adams spectral sequence.

Contacting me:

• Office: Padelford C-538
• Phone: 543-1785
• E-mail: palmieri@math.washington.edu

Go to John Palmieri's home page.

Last modified: Wed Mar 15 13:54:33 PST 2006