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Universal coefficient theorem for homology

For an abelian coefficient group

G

, there is a split short exact sequence

0 \to H_{i} (X; Z) \otimes G \to H_{i} (X; G) \to Tor (H_{i - 1} (X; Z), G) \to 0.

For

G = Q

, the Tor term vanishes.

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- Rational homology Universal coefficient theorem for homology 20

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