Rigidity versus flexibility for tight confoliations

Thomas Vogel
2011 Geometry and Topology  
In their book [10] 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 [10] negatively. Despite this, it is still possible to prove restrictions on homotopy classes of plane fields which contain tight confoliations. The failure of the Thurston-Bennequin inequalities for tight confoliations is due to the presence of overtwisted stars. Overtwisted stars
more » ... 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 overtwisted stars.
doi:10.2140/gt.2011.15.41 fatcat:d6ys72epczdylhsmnenpzowcmi