Cohomology of Courant algebroids with split base

Details Cohomology of Courant algebroids with split base Cohomology of Courant algebroids with split base

2008-05-22

arxiv.org/abs/0805.3405v2

Journal of Symplectic Geometry, vol 7.3 (2009), pp.311-335

Mathematics

Differential Geometry

28 pages, few references added

Scientific paper

We study the (standard) cohomology $H^\bullet_{st}(E)$ of a Courant algebroid $E$. We prove that if $E$ is transitive, the standard cohomology coincides with the naive cohomology $H_{naive}^\bullet(E)$ as conjectured by Stienon and Xu. For a general Courant algebroid we define a spectral sequence converging to its standard cohomology. If $E$ is with split base, we prove that there exists a natural transgression homomorphism $T_3$ (with image in $H^3_{naive}(E)$) which, together with the naive cohomology, gives all $H^\bullet_{st}(E)$. For generalized exact Courant algebroids, we give an explicit formula for $T_3$ depending only on the \v{S}evera characteristic clas of $E$.

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