Fillable structures on negative-definite Seifert fibred spaces
Geometric Topology
2026-05-01 v1 Symplectic Geometry
Abstract
We classify fillable contact structures on all negative-definite star-shaped plumbings. Along the way, we show that such Seifert fibred spaces admit a unique negative maximal twisting number, and compute it explicitly using the Alexander filtration in lattice cohomology. In particular, we show that the negative-twisting tight structures on these manifolds are induced by the Stein structures on the minimal resolution of the underlying complex surface singularity. As an application, we provide a necessary condition for a negative-definite Seifert fibred space to admit a separating contact-type embedding in a strong symplectic filling of a generalised -space.
Keywords
Cite
@article{arxiv.2604.28174,
title = {Fillable structures on negative-definite Seifert fibred spaces},
author = {Alberto Cavallo and Irena Matkovič},
journal= {arXiv preprint arXiv:2604.28174},
year = {2026}
}