The standard cohomology of regular Courant algebroids

Abstract

For any regular Courant algebroid $E$ over a smooth manifold $M$ with characteristic distribution $F$ and ample Lie algebroid $A_E$, we prove that there exists a canonical homological vector field on the graded manifold $A_E[1]\oplus (TM/F{)}^{\ast }[2]$ such that the resulting dg manifold ${\mathcal{M}}_E$, which we call the minimal model of the Courant algebroid $E$, encodes all cohomological information of $E$. Indeed, the standard cohomology of $E$ can be identified with the cohomology of the function space on ${\mathcal{M}}_E$, which can be computed by a Hodge-to-de Rham type spectral sequence. We apply this result to generalized exact Courant algebroids and those arising from regular Lie algebroids.

arXiv comment40 pages. Final version. To appear in Advances in Mathematics

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