紧密密集的刚性与柔性
Rigidity versus flexibility for tight confoliations
摘要：
在\cite{confol} Y. Eliashberg和W. Thurston给出了紧confoliations的定义。给出了一个在$T^3$上的紧褶积$ξ$不满足Thurston-Bennequin不等式的例子.这是对\cite{confol}提出的一个问题的否定回答。虽然紧密的confoliation并不意味着Thurston-Bennequin不等式，但仍然可以证明包含紧密confoliation的平面域的同伦类的限制。Thurston-Bennequin不等式在紧聚生中的失败是由于过扭曲星的存在。超扭曲星是一种特殊的勒让德曲线，它将一个圆盘的边界限定为无数个小孔。我们证明了Thurston-Bennequin不等式适用于紧confoliations没有overtwisted明星和辛填充confoliations不承认overtwisted明星。
英文摘要：
In \cite{confol} Y. Eliashberg and W. Thurston gave a definition of tight confoliations. We give an example of a tight confoliation $ξ$ on $T^3$ violating the Thurston-Bennequin inequalities. This answers a question from \cite{confol} negatively. Although the tightness of a confoliation does not imply the Thurston-Bennequin inequalities, 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 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.
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