Heegaard Floer homology and maximal twisting numbers
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866913079421304832 |
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| author | Cavallo, Alberto Matkovič, Irena |
| author_facet | Cavallo, Alberto Matkovič, Irena |
| contents | We adapt the Ozsváth-Szabó full path algorithm to every star-shaped graph and establish a correspondence between negative-twisting tight contact structures on any Seifert fibred space over $S^2$, and its Heegaard Floer homology groups equipped with the Alexander filtration induced by the regular fibre. This provides the complete classification of negative-twisting structures on these manifolds; in particular, we distinguish them by their contact invariant $c^+$. We prove that every such structure is symplectically fillable and extend a known obstruction to Stein fillability. In addition, we show that the number of negative-twisting structures can be expressed combinatorially in terms of the Seifert coefficients of the star-shaped graph, while their $d_3$-invariant and homotopy type are determined explicitly through our correspondence. Our results also complete the classification of fillable structures on any small Seifert fibred space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_28162 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Heegaard Floer homology and maximal twisting numbers Cavallo, Alberto Matkovič, Irena Geometric Topology Symplectic Geometry We adapt the Ozsváth-Szabó full path algorithm to every star-shaped graph and establish a correspondence between negative-twisting tight contact structures on any Seifert fibred space over $S^2$, and its Heegaard Floer homology groups equipped with the Alexander filtration induced by the regular fibre. This provides the complete classification of negative-twisting structures on these manifolds; in particular, we distinguish them by their contact invariant $c^+$. We prove that every such structure is symplectically fillable and extend a known obstruction to Stein fillability. In addition, we show that the number of negative-twisting structures can be expressed combinatorially in terms of the Seifert coefficients of the star-shaped graph, while their $d_3$-invariant and homotopy type are determined explicitly through our correspondence. Our results also complete the classification of fillable structures on any small Seifert fibred space. |
| title | Heegaard Floer homology and maximal twisting numbers |
| topic | Geometric Topology Symplectic Geometry |
| url | https://arxiv.org/abs/2604.28162 |