Last modified date: <%+ tp.file.last_modified_date() %>
- Tags
- Refs:
-
Links:
- Galois cohomology
- classifying space
- Cartan-Eilenberg formula
group cohomology
Definitions
If \(X\) is an aspherical space, then \(H^k_{\mathrm{sing}}(X;{\mathcal{F}}) \cong H^k_{\mathsf{Grp}}(\pi_1 X; {\mathcal{F}}_x)\) where \({\mathcal{F}}\) is a local system.
Application
See character variety: 
Interpretations
An example of a second group cohomology group is the Brauer group: it is the cohomology of the absolute Galois group of a field \(k\) which acts on the invertible elements in a separable closure: \begin{align*} H^{2}\left(\operatorname{Gal}(k),\left(k^{\text {sep }}\right)^{\times}\right) . \end{align*}
Invariants and Coinvariants
Nonabelian
Induction and Coinduction
# group cohomology
See induction
Crossed homomorphisms
Tate Cohomology
# Infty Categorical Coinvariants
The LES
Transfers
Examples
Finite cyclic groups
#examples/explicit-computations
Free groups
Pairings
Universal coefficients
