# Questions tagged [cohomology-operations]

Use this tag for questions about natural transformations from a functor defining a cohomology theory to itself. Common examples include Steenrod squares in mod 2 cohomology and Adams operations in K-theory.

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### Suspension map and Stable cohomology operation as inverse limit.

I found in the Fomenko's book that the stable cohomology operation is an inverse limit of $(H^{n+q}(K(G,n);H),f_n)$, where $G,H$ are a group (or rings, or fields for simplicity, it doesn't matter). My ...
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### On how to compute $H_*(\Omega^2 S^{n+2}, \mathbb Z/2)$ and its Steenrod operations

I've been trying to understand the calculation of $H_*(\Omega^2 S^{n+2},\mathbb Z/2)$ as an algebra, together with the dual Steenrod operations on it which lower the degrees. I've spent many hours ...
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### Why is the Bockstein morphism a derivation?

I'm trying to understand the Bockstein morphism in cohomology, and one of the points is that $\delta : H^*(G,\mathbb{F}_p)\to H^*(G,\mathbb{F}_p)$ is a derivation that squares to $0$. I could ...
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### Why does «Massey cube» of an odd element lie in 3-torsion?

The cup product is supercommutative, i.e the supercommutator $[-,-]$ is trivial at the cohomology level — but not at the cochain level, which allows one to produce various cohomology operations. The ...
By an integral cohomology operation I mean a natural transformation $H^i(X, \mathbb{Z}) \times H^j(X, \mathbb{Z}) \times ... \to H^k(X, \mathbb{Z})$, where we restrict $X$ to some nice category of ...