标题： 交数的自然基底 显示英文标题

标题： A natural basis for intersection numbers

摘要： 我们宣传初等对称多项式$e_i$作为生成系列$A_{g,n}$的自然基，这些系列是亏格 g 和 n 个标记点的交数。 已知$A_{g,n}$的闭合公式对于 genera$0$和$1$是已知的——这种方法提供了$g = 2,3,4$的公式，以及计算任何 g 的公式的算法。e_i 基础的声称自然性依赖于某些系数的意外消失，这些系数有明显的模式：我们猜想$A_{g,n}$在展开中最多可以有$g$个因子$e_i$，其中$i>1$。 这一观察促进了更一般的上同调类的范式。 作为该猜想的应用，我们找到了$A_{g,n}$的新积分表示，这些表示恢复了以贝塞尔函数形式表达的魏尔-彼得森体积。 显示英文摘要

摘要： We advertise elementary symmetric polynomials $e_i$ as the natural basis for generating series $A_{g,n}$ of intersection numbers of genus g and n marked points. Closed formulae for $A_{g,n}$ are known for genera $0$ and $1$ -- this approach provides formulae for $g = 2,3,4$, together with an algorithm to compute the formula for any g. The claimed naturality of the e_i basis relies in the unexpected vanishing of some coefficients with a clear pattern: we conjecture that $A_{g,n}$ can have at most $g$ factors $e_i$, with $i>1$, in its expansion. This observation promotes a paradigm for more general cohomology classes. As an application of the conjecture, we find new integral representations of $A_{g,n}$, which recover expressions for the Weil-Petersson volumes in terms of Bessel functions.