Stable cohomology operation

This article or section of article is sourced from:Springer Online Reference Works

This article is about a general term. A list of important particular cases (instances) is available at Category:Stable cohomology operations

Definition

A stable cohomology operation of type $(\pi ,G)$ and of degree $k$ is defined as a set $\{\theta _{n}\}_{-\infty }^{\infty }$ of cohomology operations $\theta _{n}$ of type $(n,n+k,\pi ,G)$ such that $\theta _{n-1}$ is the cohomology suspension of $\theta _{n}$.

For a stable cohomology operation, all its constituent cohomology operations are group homomorphisms (this is not true for cohomology operations in isolation).