Cohomology of courant algebroids with split base

Grégory Ginot; Melchior Grützmann

doi:10.4310/JSG.2009.v7.n3.a3

Cohomology of courant algebroids with split base

Grégory Ginot
, Melchior Grützmann

École Polytechnique

Pennsylvania State University

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

In this paper we study the cohomology H^._st(E) of a Courant algebroid E. We prove that if E is transitive, H^. _st(E) coincides with the naive cohomology H^. _naive(E) of E as conjectured by Stiénon and Xu. For general Courant algebroids E we define a spectral sequence converging to H ^._st(E). If E is with split base, we prove that there exists a natural transgression homomorphism T₃ (with image in H ³_naive(E)) which, together with H^. _naive(E), gives all H^._st(E). For generalized exact Courant algebroids, we give an explicit formula for T₃ depending only on the Ševera characteristic clas of E.

Original language	English
Pages (from-to)	311-335
Number of pages	25
Journal	Journal of Symplectic Geometry
Volume	7
Issue number	3
DOIs	https://doi.org/10.4310/JSG.2009.v7.n3.a3
Publication status	Published - 1 Jan 2009

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title = "Cohomology of courant algebroids with split base",

abstract = "In this paper we study the cohomology H.st(E) of a Courant algebroid E. We prove that if E is transitive, H. st(E) coincides with the naive cohomology H. naive(E) of E as conjectured by Sti{\'e}non and Xu. For general Courant algebroids E we define a spectral sequence converging to H .st(E). If E is with split base, we prove that there exists a natural transgression homomorphism T3 (with image in H 3naive(E)) which, together with H. naive(E), gives all H.st(E). For generalized exact Courant algebroids, we give an explicit formula for T3 depending only on the {\v S}evera characteristic clas of E.",

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AU - Grützmann, Melchior

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N2 - In this paper we study the cohomology H.st(E) of a Courant algebroid E. We prove that if E is transitive, H. st(E) coincides with the naive cohomology H. naive(E) of E as conjectured by Stiénon and Xu. For general Courant algebroids E we define a spectral sequence converging to H .st(E). If E is with split base, we prove that there exists a natural transgression homomorphism T3 (with image in H 3naive(E)) which, together with H. naive(E), gives all H.st(E). For generalized exact Courant algebroids, we give an explicit formula for T3 depending only on the Ševera characteristic clas of E.

AB - In this paper we study the cohomology H.st(E) of a Courant algebroid E. We prove that if E is transitive, H. st(E) coincides with the naive cohomology H. naive(E) of E as conjectured by Stiénon and Xu. For general Courant algebroids E we define a spectral sequence converging to H .st(E). If E is with split base, we prove that there exists a natural transgression homomorphism T3 (with image in H 3naive(E)) which, together with H. naive(E), gives all H.st(E). For generalized exact Courant algebroids, we give an explicit formula for T3 depending only on the Ševera characteristic clas of E.

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EP - 335

JO - Journal of Symplectic Geometry

JF - Journal of Symplectic Geometry

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ER -

Cohomology of courant algebroids with split base

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