 Bockstein homomorphism

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

The Bockstein homomorphism is a tool in algebraic topology, specifically in the study of cohomology theories and exact sequences of coefficients. It often appears in the context of Singular Cohomology and Cohomology with local coefficients. To understand the Bockstein homomorphism, it helps to start with the following concepts: 1. **Exact Sequence**: The Bockstein homomorphism is most commonly associated with a short exact sequence of abelian groups (or modules).