Fillable structures on negative-definite Seifert fibred spaces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866909005210714112 |
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| author | Cavallo, Alberto Matkovič, Irena |
| author_facet | Cavallo, Alberto Matkovič, Irena |
| contents | 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 $L$-space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_28174 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fillable structures on negative-definite Seifert fibred spaces Cavallo, Alberto Matkovič, Irena Geometric Topology Symplectic Geometry 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 $L$-space. |
| title | Fillable structures on negative-definite Seifert fibred spaces |
| topic | Geometric Topology Symplectic Geometry |
| url | https://arxiv.org/abs/2604.28174 |