Contact structures exist on Brieskorn spheres with non-vanishing hat Heegaard Floer contact invariant but vanishing plus version, proving the two invariants are not equivalent.
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4 Pith papers cite this work, alongside 137 external citations. Polarity classification is still indexing.
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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.
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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The hat and plus version of the Heegaard Floer contact invariant are not equivalent
Contact structures exist on Brieskorn spheres with non-vanishing hat Heegaard Floer contact invariant but vanishing plus version, proving the two invariants are not equivalent.
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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.