- Chapter 1 of Hatcher's
(unpublished) book on spectral sequences; this chapter
discusses the Serre spectral sequence, and proves the
following results from class:
- What I called "Serre's lemma" and its corollary about
the transgression: see Proposition 1.13 and Lemma 1.35.
- Borel's theorem: see Theorem 1.34.
- Serre's computation of the cohomology of Eilenberg-Mac
Lane spaces: Theorem 1.32
- Due Friday, October 12: We know that
F2) is isomorphic to the
polynomial algebra F2[x]
with x in dimension 1. Use the Cartan formula and
the instability conditions to compute
Sqi(xj) for all i and j.