Courant algebroids: Cohomology and Matched Pairs

Details Courant algebroids: Cohomology and Matched Pairs Courant algebroids: Cohomology and Matched Pairs

2010-04-09

arxiv.org/abs/1004.1487v1

Mathematics

Differential Geometry

66 pages

Scientific paper

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.

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