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{wiki=Universal_coefficient_theorem}

For an abelian coefficient group $G$, cohomology fits into a split short exact sequence
$$
0\to\operatorname{Ext}(H_{n-1}(X;\mathbb Z),G)
\to H^n(X;G)
\to\operatorname{Hom}(H_n(X;\mathbb Z),G)\to0.
$$


Universal coefficient theorem for cohomology

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 165 / 4 / i / Solution

Universal coefficient theorem for cohomology

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Universal coefficient theorem for cohomology

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