Overtwisted Disks and Exotic Symplectic Structures

TL;DR

This paper demonstrates that the symplectization of overtwisted contact structures yields exotic symplectic structures on Euclidean spaces, extending to higher dimensions using GPS-structures.

Contribution

It introduces a method to construct exotic symplectic structures from overtwisted contact structures and extends this to higher dimensions with GPS-structures.

Findings

Symplectization of overtwisted contact structures produces exotic symplectic structures.

Extension of the technique to higher dimensions using GPS-structures.

Applicable to symplectizations of open contact manifolds.

Abstract

The symplectization of an overtwisted contact structure in Euclidean 3--space is shown to be an exotic symplectic structure on Euclidean 4--space. The technique can be extended to produce exotic symplectic structures in higher dimensional Euclidean spaces using a GPS--structure and applies to symplectizations of appropriate open contact manifolds.