In this article we define intersection Floer homology for exact Lagrangian cobordisms between Legendrian submanifolds in the contactisation of a Liouville manifold, provided that the Chekanov-Eliashberg algebras of the negative ends of the cobordisms admit augmentations. From this theory we derive several exact sequences relating the Morse homology of an exact Lagrangian cobordism with the bilinearised contact homologies of its ends. These are then used to investigate the topological properties of exact Lagrangian cobordisms.

中文翻译：

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拉格朗日协边的弗洛尔理论

在本文中，我们定义了 Liouville 流形接触中勒格朗日子流形之间精确拉格朗日协边的交集 Floer 同源性，前提是协边负端的 Chekanov-Eliashberg 代数承认增广。从这个理论我们推导出几个精确序列，将精确拉格朗日坐标的莫尔斯同源性与其末端的双线性接触同源性相关联。然后将这些用于研究精确拉格朗日坐标的拓扑特性。