549KbAbstractWe give a generalization of the concept of near symplectic structures to 2n dimensions. replica hermes black berkin
According to our definition, a closed 2 form on a 2n manifold M is near symplectic, if it is symplectic outside a submanifold Z of codimension 3, where the (n 1) th power of the 2 form vanishes. We depict how this notion relates to near symplectic 4 manifolds and broken Lefschetz fibrations via some examples. We define a generalized broken Lefschetz fibration, or BLF, as a singular map with indefinite folds and Lefschetz type singularities. We show that given such a map on a 2n manifold over a symplectic base of codimension 2, then the total space carries such a near symplectic structure, whose singular locus corresponds precisely to the singularity set of the fibration. A second part studies the geometry around the codimension 3 singular locus Z. We describe a splitting property of the normal bundle N_Z that is also present in dimension four. A tubular neighbourhood for Z is provided, which has as a corollary a Darboux type theorem for near symplectic forms.