Torus bundle Liouville domains are stably Weinstein

TL;DR

This paper introduces local Liouville homotopies to simplify Liouville domain dynamics and demonstrates that certain Liouville domains are stably Weinstein, extending the understanding of symplectic topology.

Contribution

The authors develop explicit local operations on Liouville domains inspired by convex hypersurface techniques, showing that some Liouville domains are stably Weinstein.

Findings

Liouville homotopies can simplify Liouville vector field dynamics.

Certain Liouville domains are proven to be stably Weinstein.

The methods extend techniques from contact topology to Liouville domains.

Abstract

We develop explicit local operations that may be applied to Liouville domains, with the goal of simplifying the dynamics of the Liouville vector field. These local operations, which are Liouville homotopies, are inspired by the techniques used by Honda and Huang in [HH19] to show that convex hypersurfaces are $C^0$-generic in contact manifolds. As an application, we use our operations to show that certain Liouville-but-not-Weinstein domains constructed by Huang in [Hua20] are stably Weinstein.