不可定向曲面的Mirzakhani递归
A Mirzakhani recursion for non-orientable surfaces
摘要：
我们回顾Mirzakhani的递归量的模空间的定向表面，使用的角度，推广到非定向表面。不可定向的版本导致发散时，递归迭代，从区域在模空间与小crosscaps。然而，递归的积分核是定义良好的，并且它们精确地映射到具有正交对称类的矩阵积分的回路方程上，并且对于$E>0$，特征值的经典密度与$\sinh(2π\sqrt{E})$成比例。递归可用于计算具有最小横截面尺寸的截止值的正则化体积。
英文摘要：
We review Mirzakhani's recursion for the volumes of moduli spaces of orientable surfaces, using a perspective that generalizes to non-orientable surfaces. The non-orientable version leads to divergences when the recursion is iterated, from regions in moduli space with small crosscaps. However, the integral kernels of the recursion are well-defined and they map precisely onto the loop equations for a matrix integral with orthogonal symmetry class and classical density of eigenvalues proportional to $\sinh(2π\sqrt{E})$ for $E>0$. The recursion can be used to compute regularized volumes with a cutoff on the minimal size of a crosscap.
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