论文标题
Mirzakhani卷及其超级扩展的简单递归
A Simple Recursion for the Mirzakhani Volume and its Super Extension
论文作者
论文摘要
在本文中，我们得出了一个简单的递归公式，用于具有边界双曲线表面的模量空间的Weil-Petersson体积。该公式证明了体积函数的多项式性。通过为原始公式和我们的替代公式构建拉普拉斯变换，我们表明它们是直接等效的。通过考虑这些公式的顶级和最低度术语，我们恢复了$ \ Mathcal {M} _ {g，n} $的DVV身份和共同体类别标识。为这些结果的超级分析得出了类似的结论。
In this paper, we derive a simple recursion formula for the Weil-Petersson volumes of moduli spaces of hyperbolic surfaces with boundaries. This formula demonstrates the polynomiality of the volume functions. By constructing the Laplace transform for both the original and our alternative formulas, we show that they are directly equivalent. By considering the top and lowest degree terms of these formulas, we recover the DVV identity and cohomology class identities for $\mathcal{M}_{g,n}$. Similar conclusions are drawn for the super-analog of these results.
