Polyfolds, Cobordisms, and the strong Weinstein conjecture

TL;DR

This paper proves the strong Weinstein conjecture for certain closed contact manifolds that are boundaries of symplectic cobordisms with a special foliation by holomorphic spheres.

Contribution

It establishes the conjecture for a new class of contact manifolds using symplectic and holomorphic foliation techniques.

Findings

Proves the strong Weinstein conjecture in the specified setting.

Identifies conditions on symplectic cobordisms that imply the conjecture.

Utilizes holomorphic sphere foliations to derive the result.

Abstract

We prove the strong Weinstein conjecture for closed contact manifolds that appear as the concave boundary of a symplectic cobordism admitting an essential local foliation by holomorphic spheres.