Cyclic A-infinity algebras and their Koszul duals

循环A-无穷代数的概念自然地出现在许多代数和拓扑学的上下文中，例如作为Poincare对偶空间的余链代数。重要的是要从本质上描述他们的科祖尔对偶。这种描述是在Van den Berg最近的工作中提供的，但只是在相当严格的分级假设下提供的，特别是排除了上面提到的例子。这个项目的目标是去掉这些假设，并将刻画细化到对易情形。一个推论是Poincare对偶空间的同伦李代数的内在刻画。

The notion of a cyclic A-infinity algebra appears naturally in many contexts of algebra and topology, e.g. as cochain algebras of Poincare duality spaces. It is important to characterize intrinsically their Koszul duals. Such a characterization was provided in a recent work of Van den Berg but inly under rather restrictive grading assumptions that are, in particular, exclude the example mentioned above. The goal of this project is to remove these assumptions and also refine the characterization to the commutative case. A corollary would be an intrinsic characterization of homotopy Lie algebras of Poincare duality spaces.