Bockstein homomorphism (source code)

= Bockstein homomorphism
{c}
{title2=$\beta$}
{wiki}

The Bockstein homomorphism is the connecting homomorphism associated with a short exact sequence of coefficient groups. For $0\to\mathbb Z/n\to\mathbb Z/n^2\to\mathbb Z/n\to0$, it has degree $-1$ on homology and degree $+1$ on cohomology.