# An Invitation to Singular Symplectic Geometry

## TL;DR

This paper explores advanced structures in symplectic geometry, including $b^m$-symplectic forms, models in Celestial Mechanics, and introduces $b$-contact manifolds as an odd-dimensional analogue.

## Contribution

It provides detailed examples, models in Celestial Mechanics, and introduces the concept of $b$-contact manifolds, expanding the framework of symplectic geometry.

## Key findings

- Models for $b^m$-symplectic structures in Celestial Mechanics
- Introduction of $b$-contact manifolds as odd-dimensional analogues
- Detailed analysis of $b^m$-symplectic forms and folded symplectic structures

## Abstract

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