论文标题
开放式R-Spin理论I：基础
Open r-spin theory I: Foundations
论文作者
论文摘要
我们为带边界的Riemann表面的$ r $ spin理论奠定了基础。特别是，我们定义了$ r $ -spin磁盘，它们的模量空间和Witten捆绑包的概念，我们表明模量空间是一个紧凑的平滑光滑方向的Orbifold，其角落，我们证明Witten Bundle是相对于Moduli空间的规范上相对方向的。在本文的续集中，我们使用这些构造来定义开放的$ r $ -spin交叉路口理论，并将其与Gelfand-Dickey层次结构相关联，从而在开放环境中提供了Witten的$ R $ -SPIN猜想的类似物。
We lay the foundation for a version of $r$-spin theory in genus zero for Riemann surfaces with boundary. In particular, we define the notion of $r$-spin disks, their moduli space, and the Witten bundle, we show that the moduli space is a compact smooth orientable orbifold with corners, and we prove that the Witten bundle is canonically relatively oriented relative to the moduli space. In the sequel to this paper, we use these constructions to define open $r$-spin intersection theory and relate it to the Gelfand-Dickey hierarchy, thus providing an analogue of Witten's $r$-spin conjecture in the open setting.
