Atiyah–Hirzebruch spectral sequence

In mathematics, the Atiyah–Hirzebruch spectral sequence is a spectral sequence for calculating generalized cohomology, introduced by Atiyah & Hirzebruch (1961) in the special case of topological K-theory. For a CW complex ${\displaystyle X}$ and a generalized cohomology theory ${\displaystyle E^{\bullet }}$, it relates the generalized cohomology groups

with 'ordinary' cohomology groups ${\displaystyle H^{j}}$ with coefficients in the generalized cohomology of a point. More precisely, the ${\displaystyle E_{2}}$ term of the spectral sequence is ${\displaystyle H^{p}(X;E^{q}(pt))}$, and the spectral sequence converges conditionally to ${\displaystyle E^{p+q}(X)}$.

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