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.
Colin,Chirurgies d’indice un et isotopies de sphéres dans les variétés de contact tendues, C
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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.