Projecte: Deformations, cobordisms and Levi-flat structures in generalized geometry

The expected contribution of this proposal is manifold. First, to solve the Dirac complement problem and explore its consequences in deformation theory
and the moduli space of Dirac structures. Second, to establish the theory of generalized cobordisms and apply it both in the generalized and the classical
(in relation to symplectic cobordisms) setup. Third, to find a complete set of invariants of B3-generalized complex structures, prove or disprove and hprinciple
for these structures and determine their relation with these structures with the topology and geometry of 3 and 5-manifolds. And fourth, to
understand how generalized structures come together from its classical geometric components and propose a setup that is generically complex. This,
together with deformation theory, will open the door to tackle the open question of the existence of Levi-flat structures on odd-dimensional spheres.