论文标题
无与伦比填充的紧密接触结构无处不在
Tight contact structures without symplectic fillings are everywhere
论文作者
论文摘要
我们表明，对于所有$ n \ geq 3 $，任何$（2N+1）$ - 尺寸歧管，它承认紧密的接触结构，也承认在相同的几乎接触类中也承认紧密但不可填充的接触结构。对于$ n = 2 $，我们获得相同的结果，只要Chern Class消失了。我们进一步构建了liouville，但在任何Weinstein填充的接触结构上都不是在Weinstein的任何可填充尺寸的可填充接触歧管上，至少$ 7 $与Torsion First Chern类别。
We show that for all $n \geq 3$, any $(2n+1)$-dimensional manifold that admits a tight contact structure, also admits a tight but non-fillable contact structure, in the same almost contact class. For $n=2$, we obtain the same result, provided that the first Chern class vanishes. We further construct Liouville but not Weinstein fillable contact structures on any Weinstein fillable contact manifold of dimension at least $7$ with torsion first Chern class.
