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About: Bockstein homomorphism     Goto   Sponge   NotDistinct   Permalink

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In homological algebra, the Bockstein homomorphism, introduced by Meyer Bockstein , is a connecting homomorphism associated with a short exact sequence of abelian groups, when they are introduced as coefficients into a chain complex C, and which appears in the homology groups as a homomorphism reducing degree by one, To be more precise, C should be a complex of free, or at least torsion-free, abelian groups, and the homology is of the complexes formed by tensor product with C (some flat module condition should enter). The construction of β is by the usual argument (snake lemma). ,;