Subflexible symplectic manifolds

TL;DR

This paper introduces a new class of Weinstein domains called subflexible symplectic manifolds, which are sublevel sets of flexible Weinstein manifolds but are not flexible themselves, revealing nuanced behaviors in symplectic topology.

Contribution

It defines subflexible Weinstein domains, constructs numerous examples, and shows that any flexible Weinstein manifold can be homotoped to include a nonflexible sublevel set.

Findings

Subflexible Weinstein domains are not flexible but share some properties.

Examples demonstrate the subtle behavior of these manifolds with respect to holomorphic curves.

Any flexible Weinstein manifold can be modified to contain a nonflexible sublevel set.

Abstract

We introduce a class of Weinstein domains which are sublevel sets of flexible Weinstein manifolds but are not themselves flexible. These manifolds exhibit rather subtle behavior with respect to both holomorphic curve invariants and symplectic flexibility. We construct a large class of examples and prove that every flexible Weinstein manifold can be Weinstein homotoped to have a nonflexible sublevel set.