David Martínez, Universidad Carlos III de Madrid
Odd dimensional almost complex geometry

Approximately holomorphic techniques were introduced by Donaldson to prove the existence of symplectic submanifolds in compact symplectic manifolds. Further generalizations led to different constructions as Lefschetz pencils (Donaldson), normal forms for maps to CP2 (Auroux), embeddings to CPN (Muñoz, Presas, Sols). Here we will present a joint work (Ibort, Martínez-Torres, Presas) that extends some of the known results for symplectic manifolds to its odd dimensional counterparts.