Serre Spectral Sequence
Filtering the cohomology of a fibration F → E → B page by page
Fibration
Hopf: S¹→S³→S²
ΩS²→PS²→S²
Z→R→S¹
S¹→T²→S¹
Page r =
E₂
E_r^{p,q} grid
Each cell (p,q) holds
E_r^{p,q}
. Differential
d_r: E_r^{p,q} → E_r^{p+r,q-r+1}
. The sequence converges:
E_∞^{p,q} ⇒ H^{p+q}(E)
.