Presymplectic manifolds

TL;DR

This paper explores the geometry of presymplectic manifolds, providing foundational theorems and methods for constructing and modifying them, including gluing and surgery techniques.

Contribution

It introduces new theorems and methods for constructing presymplectic manifolds, extending analogies from symplectic and contact topology.

Findings

Established basic theorems for presymplectic manifolds

Developed techniques for gluing presymplectic manifolds

Described surgery procedures along presymplectic circles

Abstract

A presymplectic structure on odd dimensional manifold is given by a closed 2-form which is nondegenerate, i.e., of maximal rank. We investigate geometry of presymplectic manifolds. Some basic theorems analogous to those in symplectic and contact topology are given and applied to study constructions of presymplectic manifolds. In particular, we describe how to glue presymplectic manifolds along a presymplectic submanifold, including surgery along a presymplectic circles.