Atiyah-Hirzebruch spectral sequence
= Atiyah-Hirzebruch spectral sequence
{c}
{title2=$E_2^{s,t}=H^s(X;h^t(\mathrm{pt}))\Longrightarrow h^{s+t}(X)$}
The skeletal filtration of a CW complex gives this spectral sequence, with differential of bidegree $(r,1-r)$ in cohomological grading. For a finite complex the filtration is finite and convergence is bounded. In a multiplicative theory the associated graded product is the ordinary cohomology product with coefficients in the theory's coefficient ring.