We establish some fundamental relations between Dirac subbundles L for the generalized Courant algebroid (A⊕A, φ+W ) over a differentiable manifold M and the associated Dirac subbubndles L̃ for the corresponding Courant algebroid Ã⊕ Ã over M × IR.

The question of determining for which eigenvalues there exists an eigenfunction has the same number nodal domains as label associated eigenvalue (Courant-sharp property) was motivated by analysis minimal spectral partitions. In previous works, many examples have been analyzed corresponding to squares, rectangles, disks, triangles, tori, \ldots . A natural toy model further investigations is M\"...

In categorified symplectic geometry, one studies the categorified algebraic and geometric structures that naturally arise on manifolds equipped with a closed nondegenerate (n + 1)-form. The case relevant to classical string theory is when n = 2 and is called ‘2-plectic geometry’. Just as the Poisson bracket makes the smooth functions on a symplectic manifold into a Lie algebra, there is a Lie 2...

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 [SX08]. 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 (wit...

In categorified symplectic geometry, one studies the categorified algebraic and geometric structures that naturally arise on manifolds equipped with a closed non-degenerate n + 1-form. The case relevant to classical string theory is when n = 2 and is called ‘2-plectic geometry’. Just as the Poisson bracket makes the smooth functions on a symplectic manifold into a Lie algebra, there is a Lie 2-...