An overtwisted disk in a virtual contact structure and the Weinstein conjecture

TL;DR

This paper extends the Weinstein conjecture proof from overtwisted disks in contact 3-manifolds to virtual contact structures, introducing a new example via Lutz twist.

Contribution

It generalizes the Weinstein conjecture to virtual contact structures and constructs an explicit example with an overtwisted disk.

Findings

Extended Weinstein conjecture to virtual contact structures

Constructed a new explicit example with a Lutz twist

Confirmed overtwisted disks imply the conjecture in this setting

Abstract

Hofer proved the Weinstein conjecture for a closed contact 3-manifold with an overtwisted disk. In this article we extend it to the virtual contact structure and provide a new explicit example of the virtual contact structure with an overtwisted disk via a Lutz twist.