Abstract

While contact geometry is often described as the odd-dimensional analogue of symplectic geometry, Arnol'd pointed out that the relation between these two geometries is analogous to that between affine and projective geometries. A natural (vague!) question is to investigate the extent to which this analogy extends to the degenerate versions of symplectic and contact structures, namely Poisson and Jacobi geometries. The aim of this talk is to attempt to formalise the above question and to illustrate the intimate relation between these six geometries through a few specific problems, including isotropic realisations and Poisson/Jacobi manifolds of compact types. The talk is based on joint work with María Amelia Salazar, and on ongoing joint work with Camilo Angulo and María Amelia Salazar.