Geometry and representation of the singular symplectic forms
Volume 62 / 2003
Banach Center Publications 62 (2003), 57-71
MSC: Primary 57R45; Secondary 58A10
DOI: 10.4064/bc62-0-4
Abstract
In this paper we show to what extent the closed, singular $2$-forms are represented, up to the smooth equivalence, by their restrictions to the corresponding singularity set. In the normalization procedure of the singularity set we find the sufficient conditions for the given closed $2$-form to be a pullback of the classical Darboux form. We also find the classification list of simple singularities of the maximal isotropic submanifold-germs in the codimension one Martinet's singular symplectic structures. An example of the exotic singular symplectic structure-germ with no existence of Lagrangian germs is constructed and the singularity theory framework for the pulled back singular symplectic forms is provided.
