论文标题
Morse-Bott设置中的计算嵌入式接触同源性
Computing Embedded Contact Homology in Morse-Bott Settings
论文作者
论文摘要
鉴于触点三个歧管$ y $，带有非排效公司触点$λ$，而几乎复杂的结构$ j $与$λ$兼容，其embedded Contact toctuct tocture同源$ ECH（y，λ）$被定义（ARXIV：1303.5789），仅取决于接触结构。在本文中，我们解释了如何计算莫尔斯 - 巴特接触形式的ECH，其Reeb Orbits出现在$ s^1 $系列中，假设可以选择几乎复杂的结构$ J $以满足某些横向条件（例如，对于凹形或convex toric域的界限，或者是ech Index Index Index One属的曲线）。我们通过枚举ECH指数一级级联来定义莫尔斯 - 北部接触形式的ECH链复合体。我们证明使用Arxiv：2206.04334的胶合结果表明，该链复合物计算触点歧管的ECH。本文和Arxiv：2206.04334填写了文献中先前计算的一些技术基础（Arxiv：1608.07988，Arxiv：Math/0410061）。
Given a contact three manifold $Y$ with a nondegenerate contact form $λ$, and an almost complex structure $J$ compatible with $λ$, its embedded contact homology $ECH(Y,λ)$ is defined (arXiv:1303.5789) and only depends on the contact structure. In this paper we explain how to compute ECH for Morse-Bott contact forms whose Reeb orbits appear in $S^1$ families, assuming the almost complex structure $J$ can be chosen to satisfy certain transversality conditions (this is the case for instance for boundaries of concave or convex toric domains, or if all the curves of ECH index one have genus zero). We define the ECH chain complex for a Morse-Bott contact form via an enumeration of ECH index one cascades. We prove using gluing results from arXiv:2206.04334 that this chain complex computes the ECH of the contact manifold. This paper and arXiv:2206.04334 fill in some technical foundations for previous calculations in the literature (arXiv:1608.07988, arXiv:math/0410061).
