Courant algebroids: Cohomology and Matched Pairs
Differential Geometry
2010-04-12 v1 Symplectic Geometry
Abstract
We introduce Courant algebroids, providing definitions, some historical notes, and some elementary properties. Next, we summarize basic properties of graded manifolds. Then, drawing on the work of Roytenberg and others, we introduce the graded or supergraded language demonstrating a cochain complex / cohomology for (general) Courant algebroids. We review spectral sequences and show how this tool is used to compute cohomology of regular Courant algebroids with a split base. Finally we analyze matched pairs of Courant algebroids including the complexified standard Courant algebroid of a complex manifold, the matched pair arising from a holomorphic Courant algebroid, and certain cases of regular Courant algebroids.
Cite
@article{arxiv.1004.1487,
title = {Courant algebroids: Cohomology and Matched Pairs},
author = {Melchior Grützmann},
journal= {arXiv preprint arXiv:1004.1487},
year = {2010}
}
Comments
66 pages