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.
Title resolution pending
5 Pith papers cite this work. Polarity classification is still indexing.
5
Pith papers citing it
citation-role summary
background 1
citation-polarity summary
fields
math.GT 5years
2026 5roles
background 1polarities
background 1representative citing papers
Brieskorn spheres Σ(a1,...,an) obstruct rational homology ball symplectic fillings for any contact structure on -Y when n=3 or without half convex Giroux torsion for n>3, with limited exceptions for Milnor fillable cases, and those with vanishing correction terms have at most two fillable 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.
Provides the complete list of Brieskorn spheres carrying at most two symplectically fillable contact structures up to isotopy.
citing papers explorer
-
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.
-
Brieskorn spheres and rational homology ball symplectic fillings
Brieskorn spheres Σ(a1,...,an) obstruct rational homology ball symplectic fillings for any contact structure on -Y when n=3 or without half convex Giroux torsion for n>3, with limited exceptions for Milnor fillable cases, and those with vanishing correction terms have at most two fillable structures
-
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.
-
Brieskorn spheres with two fillable contact structures
Provides the complete list of Brieskorn spheres carrying at most two symplectically fillable contact structures up to isotopy.
- Fillable structures on negative-definite Seifert fibred spaces