An invitation to singular symplectic geometry

Abstract

In this paper, we analyze in detail a collection of motivating examples to consider [Formula: see text]-symplectic forms and folded-type symplectic structures. In particular, we provide models in Celestial Mechanics for every [Formula: see text]-symplectic structure. At the end of the paper, we introduce the odd-dimensional analogue to [Formula: see text]-symplectic manifolds: [Formula: see text]-contact manifolds.