论文标题
分类枚举不变性，i：字符串顶点
Categorical Enumerative Invariants, I: String vertices
论文作者
论文摘要
我们将组合对应物定义为Sen-Zwiebach和Costello-Zwiebach的几何字符串顶点，它们是曲线模量空间的某些封闭子集。我们的组合顶点包含与几何信息相同的信息，可有效地计算，并在循环$ a_ \ infty $ -Algebra的Hochschild链上作用。 这是一系列两篇论文中的第一篇，我们定义了与由环状$ a_ \ infty $ -Algebra组成的一对相关的枚举不变性，并在其环状同源性上对霍奇过滤进行了分裂。这些不变的人猜想从象征性的几何形状中概括了gromov-witten和fan-jarvis-ruan-witten的不变式，以及来自Holomorphic几何形状的Bershadsky-cecotti-oguri-vafa不变性。
We define combinatorial counterparts to the geometric string vertices of Sen-Zwiebach and Costello-Zwiebach, which are certain closed subsets of the moduli spaces of curves. Our combinatorial vertices contain the same information as the geometric ones, are effectively computable, and act on the Hochschild chains of a cyclic $A_\infty$-algebra. This is the first in a series of two papers where we define enumerative invariants associated to a pair consisting of a cyclic $A_\infty$-algebra and a splitting of the Hodge filtration on its cyclic homology. These invariants conjecturally generalize the Gromov-Witten and Fan-Jarvis-Ruan-Witten invariants from symplectic geometry, and the Bershadsky-Cecotti-Ooguri-Vafa invariants from holomorphic geometry.
