Bockstein homomorphism

Summary

The Bockstein homomorphism is the connecting map in the long exact sequence of (co)homology that comes from a short exact sequence of coefficient groups. It raises cohomological degree by one. For the sequence $0 \to \Z/p \to \Z/p^2 \to \Z/p \to 0$ it gives a natural operation on mod $p$ cohomology that detects $p$-torsion in integral cohomology.