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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Classifies fillable contact structures on negative-definite Seifert fibred spaces, computes unique negative maximal twisting number via lattice cohomology, and links tight structures to Stein resolutions.
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
Classifies fillable contact structures on negative-definite Seifert fibred spaces, computes unique negative maximal twisting number via lattice cohomology, and links tight structures to Stein resolutions.
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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.