group cohomology, nonabelian group cohomology, Lie group cohomology
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
Calabi-Yau cohomology is complex oriented generalized cohomology theory whose associated formal group is an Artin-Mazur formal group $\Phi^n_X$ of a Calabi-Yau variety $X$ of dimension $n$. (Which means e.g. complex dimension if working over the complex numbers).
As special cases this includes:
for $n = 0$: complex K-theory;
for $n = 1$: elliptic cohomology;
for $n = 2$: K3-cohomology.
moduli spaces of line n-bundles with connection on $n$-dimensional $X$
The general idea of Calabi-Yau cohomology apparently appears in
The suggestion that from the point of view of string theory/F-theory K3-cohomology and further Calabi-Yau cohomology this is the required generalization of elliptic cohomology appears in
Last revised on July 19, 2015 at 18:19:27. See the history of this page for a list of all contributions to it.