# Tagged Questions

251 views

### Explicit 2-Cocycles of G=Z2×Z2xZ2 over U(1)

We know that group cohomology $H^2(G,U(1))$ consists of 2-cocycles $\beta(A,B)\in U(1)$ corresponding to elements in the group $H^2(G,U(1))$, where $A\in G,B \in G$. Note that $\beta(A,B)$ satisfies ...
1k views

### Kuenneth-formula for group cohomology with nontrivial action on the coefficient

For a trivial action on the coefficient, we have the following Kuenneth formula for group cohomology:  H^n(G_1 \times G_2; M) \cong [\oplus_{i= 0}^n H^i(G_1;M) \otimes_M H^{n-i}(G_2;M)] \oplus ...
It is known that group cohomology class $H^d[U(1),Z]$ is Z for even d and 0 for odd d. Do we know $H^d[G,Z]$ for $G=SO(3)$, $SU(2)$ and other compact Lie group? Also is the Borel-group-cohomology ...
### Calculate the group cohomology classes $H^d[U(1)\rtimes Z_2, Z]$ and $H^d[U(1)\rtimes Z_2, Z_T]$
I would like to know what are the group cohomology classes $H^d[U(1)\rtimes Z_2, Z]$ and $H^d[U(1)\rtimes Z_2, Z_T]$, and/or how to calculate them. It can be shown that $H^d[U(1), Z]$ is $Z$ for ...