Links

• Chapter 1 of Hatcher's (unpublished) book on spectral sequences; this chapter discusses the Serre spectral sequence, and proves the following results from class: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

Homework

• Due Friday, October 12: We know that H^*(K(Z/2Z,1); 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(x^j) for all i and j.