Stable cohomology operation: Difference between revisions

Latest revision as of 19:59, 11 May 2008

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

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

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-{{source|[[sor:C/c023150|Springer Online Reference Works]]}}
+{{source|[[sor:C/c023150.htm|Springer Online Reference Works]]}}
+{{particularcases|[[:Category:Stable cohomology operations]]}}
 ==Definition==
-A '''stable cohomology operation''' of ''type'' <math>(\pi,G)</math> and of ''degree'' <math>k</math> is defined as
+A '''stable cohomology operation''' of ''type'' <math>(\pi,G)</math> and of ''degree'' <math>k</math> is defined as a set <math>\{ \theta_n \}_{-\infty}^{\infty}</math> of [[cohomology operation]]s <math>\theta_n</math> of type <math>(n,n+k,\pi,G)</math> such that <math>\theta_{n-1}</math> is the [[cohomology suspension]] of <math>\theta_n</math>.
+For a stable cohomology operation, all its constituent cohomology operations are group homomorphisms (this is not true for [[cohomology operation]]s in isolation).