In this article we describe an algebraic framework which can be used in three related but different contexts: string topology, symplectic field theory, and Lagrangian Floer theory of higher genus. It turns out that the relevant algebraic structure for all three contexts is a homotopy version of involutive bi-Lie algebras, which we call IBL$_\infty$-algebras.

中文翻译：

---

与有边界的曲面相关的同调代数

在本文中，我们描述了一个代数框架，该框架可用于三个相关但不同的上下文：弦拓扑、辛场论和高等属的拉格朗日弗洛尔理论。事实证明，所有三个上下文的相关代数结构是对合双李代数的同伦版本，我们称之为 IBL$_\infty$-algebras。