group cohomology, nonabelian group cohomology, Lie group cohomology
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
The Schur multiplier of a group, $G$, is $H^2(G;\mathbb{C}^{\times}) \cong H^3(G;\mathbb{Z})$. It is also the second homology group, $H_2(G; \mathbb{Z})$ with coefficients in the trivial $G$-module $\mathbb{Z}$.
A group is called perfect if its abelianization is trivial, i.e., its first homology group, $H_1(G; \mathbb{Z})$, vanishes, and a perfect group is called superperfect if its Schur multiplier also vanishes.
Let $G$ be a perfect discrete group. Then $G$ possesses a Schur cover, whose central subgroup is the Schur multiplier $A_{uni} = H_2(G; \mathbb{Z})$.
Created on May 31, 2016 at 11:56:56. See the history of this page for a list of all contributions to it.