论文标题
开放$ r $ - 速键理论III：高级属的预测
Open $r$-spin theory III: a prediction for higher genus
论文作者
论文摘要
在之前的两篇论文中，我们在零属中构建了一个$ r $ spin的理论，用于带边界的里曼表面，并充分确定了相应的相交数字，从而提供了Witten的$ r $ -spin猜想在开放环境中的零属。特别是，我们证明了开放$ R $ -SPIN交集的生成系列由Gelfand-Dickey层次结构的特定扩展的特殊解决方案的属零部分确定，并且我们推测整个解决方案控制所有属的开放$ R $ - SPIN交叉数字，该属中尚未具有几何学定义。在本文中，我们提供了这种猜想的正确性的几何和代数证据。
In our previous two papers, we constructed an $r$-spin theory in genus zero for Riemann surfaces with boundary and fully determined the corresponding intersection numbers, providing an analogue of Witten's $r$-spin conjecture in genus zero in the open setting. In particular, we proved that the generating series of open $r$-spin intersection numbers is determined by the genus-zero part of a special solution of a certain extension of the Gelfand-Dickey hierarchy, and we conjectured that the whole solution controls the open $r$-spin intersection numbers in all genera, which do not yet have a geometric definition. In this paper, we provide geometric and algebraic evidence for the correctness of this conjecture.
