Negative-definite Seifert fibered spaces have a unique negative maximal twisting number, with their fillable tight contact structures induced by Stein structures on the minimal resolution of the underlying complex surface singularity.
Ghiggini,Ozsváth-Szabó invariants and fillability of contact structures, Math
3 Pith papers cite this work. Polarity classification is still indexing.
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A correspondence between negative-twisting tight contact structures on Seifert fibered spaces over S² and Alexander-filtered Heegaard Floer homology provides their complete classification, proves symplectic fillability, and gives combinatorial counts via Seifert coefficients.
Mazur manifolds with boundaries Σ(2,3,13), Σ(2,5,7), and Σ(3,4,5) admit no symplectic structure, producing exotic pairs of simply connected 4-manifolds with definite intersection forms.
citing papers explorer
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Fillable structures on negative-definite Seifert fibred spaces
Negative-definite Seifert fibered spaces have a unique negative maximal twisting number, with their fillable tight contact structures induced by Stein structures on the minimal resolution of the underlying complex surface singularity.
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Heegaard Floer homology and maximal twisting numbers
A correspondence between negative-twisting tight contact structures on Seifert fibered spaces over S² and Alexander-filtered Heegaard Floer homology provides their complete classification, proves symplectic fillability, and gives combinatorial counts via Seifert coefficients.
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Mazur manifolds and symplectic structures
Mazur manifolds with boundaries Σ(2,3,13), Σ(2,5,7), and Σ(3,4,5) admit no symplectic structure, producing exotic pairs of simply connected 4-manifolds with definite intersection forms.