The combinatorial formula for open gravitational descendents

IF 1.7 1区数学 Q1 MATHEMATICS

Geometry & Topology Pub Date : 2023-09-19 DOI:10.2140/gt.2023.27.2497

Ran J. Tessler

引用次数: 18

Abstract

In recent works, [20],[21], descendent integrals on the moduli space of Riemann surfaces with boundary were defined. It was conjectured in [20] that the generating function of these integrals satisfies the open KdV equations. In this paper we develop the notions of symmetric Strebel-Jenkins differentials and of Kasteleyn orientations for graphs embedded in open surfaces. In addition we write an explicit expression for the angular form of the sum of line bundles. Using these tools we prove a formula for the descendent integrals in terms of sums over weighted graphs. Based on this formula, the conjecture of [20] was proved in [5].

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开放重力下降的组合公式

在最近的研究中，定义了具有边界的Riemann曲面模空间上的[20]，[21]，下降积分。在[20]中推测这些积分的生成函数满足开KdV方程。在本文中，我们发展了对称Strebel-Jenkins微分和嵌入在开放曲面上的图的Kasteleyn取向的概念。此外，我们还写出了线束和的角形式的显式表达式。利用这些工具，我们证明了加权图上的和的派生积分公式。基于此公式，在[5]中证明了[20]的猜想。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Geometry & Topology MATHEMATICS-

CiteScore

3.00

自引率

5.00%

发文量

审稿时长

>12 weeks

期刊介绍： Geometry and Topology is a fully refereed journal covering all of geometry and topology, broadly understood. G&T is published in electronic and print formats by Mathematical Sciences Publishers. The purpose of Geometry & Topology is the advancement of mathematics. Editors evaluate submitted papers strictly on the basis of scientific merit, without regard to authors" nationality, country of residence, institutional affiliation, sex, ethnic origin, or political views.