Courant algebroids: Cohomology and Matched Pairs - Mathematics > Differential GeometryReport as inadecuate




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Abstract: We introduce Courant algebroids, providing definitions, some historicalnotes, and some elementary properties. Next, we summarize basic properties ofgraded manifolds. Then, drawing on the work of Roytenberg and others, weintroduce the graded or supergraded language demonstrating a cochain complex -cohomology for general Courant algebroids. We review spectral sequences andshow how this tool is used to compute cohomology of regular Courant algebroidswith a split base. Finally we analyze matched pairs of Courant algebroidsincluding the complexified standard Courant algebroid of a complex manifold,the matched pair arising from a holomorphic Courant algebroid, and certaincases of regular Courant algebroids.



Author: Melchior Gr├╝tzmann

Source: https://arxiv.org/



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