论文标题
从级联到$ j $ - 霍尔型曲线，然后返回
From Cascades to $J$-holomorphic Curves and Back
论文作者
论文摘要
本文开发了在某些情况下，建立嵌入式触点同源性（ECH）的嵌入式触点同源性（ECH）所需的分析。特别地，我们在摩尔斯 - 底接触形式的符合性中建立了霍明态曲线的“级联”与群体扰动触点扰动的符合形式的群体曲线之间的对应关系。我们认为的级联必须横向切割和僵硬。我们通过研究$ j $ holomormormormormormormormorphic曲线的绝热变性来实现这一目标，并建立粘合定理。我们注意到，我们满足适当横向假设的粘合定理也应在更高的维度上起作用。 ECH应用程序的详细信息将出现在其他地方。
This paper develops the analysis needed to set up a Morse-Bott version of embedded contact homology (ECH) of a contact three-manifold in certain cases. In particular we establish a correspondence between "cascades" of holomorphic curves in the symplectization of a Morse-Bott contact form, and holomorphic curves in the symplectization of a nondegenerate perturbation of the contact form. The cascades we consider must be transversely cut out and rigid. We accomplish this by studying the adiabatic degeneration of $J$-holomorphic curves into cascades and establishing a gluing theorem. We note our gluing theorem satisfying appropriate transversality hypotheses should work in higher dimensions as well. The details of ECH applications will appear elsewhere.
