We introduce the notion of asymptotically finitely generated contact structures, which states essentially that the Symplectic Homology in a certain degree of any filling of such contact manifolds is uniformly generated by only finitely many Reeb orbits. This property is used to generalize a famous result by Ustilovsky: We show that in a large class of manifolds (including all unit cotangent bundles and all Weinstein fillable contact manifolds with torsion first Chern class) each carries infinitely many exactly fillable contact structures. These are all different from the ones constructed recently by Lazarev. Along the way, the construction of Symplectic Homology is made more general. Moreover, we give a detailed exposition of Cieliebak’s Invariance Theorem for subcritical handle attaching, where we provide explicit Hamiltonians for the squeezing on the handle.

中文翻译：

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在具有无限多个可填充接触结构的歧管上

我们引入了渐近有限生成的接触结构的概念，该概念实质上表明，在这种接触流形的任何填充的一定程度上，辛同调仅由有限多个 Reeb 轨道均匀生成。这个性质用于概括 Ustilovsky 的一个著名结果：我们表明，在一大类流形中（包括所有单位余切丛和所有具有扭转第一陈类的 Weinstein 可填充接触流形），每个流形都带有无限多个完全可填充的接触结构。这些都与拉扎列夫最近建造的不同。一路走来，辛同调的构造变得更加普遍。此外，我们详细阐述了用于亚临界手柄附着的 Ciliebak 不变定理，