Abstract
In (9) Y. Eliashberg and W. Thurston gave a definition of tight confoliations. We give an example of a tight confoliation on T 3 violating the Thurston-Bennequin inequalities. This answers a question from (9) negatively. Despite of this, it is still possible to prove restric- tions on homotopy classes of plane fields which contain tight confolia- tions. The failure of the Thurston-Bennequin inequalities for tight confoli- ations is due to the presence of overtwisted stars. Overtwisted stars are particular configurations of Legendrian curves which bound a disc with finitely many punctures on the boundary. We prove that the Thurston- Bennequin inequalities hold for tight confoliations without overtwisted stars and that symplectically fillable confoliations do not admit over- twisted stars.
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