Non-fillability of overtwisted contact manifolds via polyfolds
Symplectic Geometry
2025-04-29 v3
Abstract
We prove that any weakly symplectically fillable contact manifold is tight. Furthermore we verify the strong Weinstein conjecture for contact manifolds that appear as the concave boundary of a directed symplectic cobordism whose positive boundary satisfies the weak-filling condition and is overtwisted. Similar results are obtained in the presence of bordered Legendrian open books whose binding-complement has vanishing second Stiefel-Whitney class. The results are obtained via polyfolds.
Keywords
Cite
@article{arxiv.2011.02249,
title = {Non-fillability of overtwisted contact manifolds via polyfolds},
author = {Wolfgang Schmaltz and Stefan Suhr and Kai Zehmisch},
journal= {arXiv preprint arXiv:2011.02249},
year = {2025}
}
Comments
Accepted for publication in Arnold Math. J