Fillable structures on negative-definite Seifert fibred spaces

Alberto Cavallo; Irena Matkovič

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arXiv · 2604.28174

Fillable structures on negative-definite Seifert fibred spaces

Alberto Cavallo·Irena Matkovič

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Abstract

We classify fillable contact structures on all negative-definite star-shaped plumbings. 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, providing its first Floer-theoretic interpretation. In addition, we show that all 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 $L$-space.

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Alberto Cavallo, Irena Matkovič. 2026-04-30. Fillable structures on negative-definite Seifert fibred spaces. https://arxiv.org/abs/2604.28174

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