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.
Wu,Legendrian vertical circles in small Seifert spaces, Commun
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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.
- Fillable structures on negative-definite Seifert fibred spaces