Presymplectic manifolds
Boguslaw Hajduk, Rafal Walczak

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.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory
