摘要翻译：
本文首先描述了圆弧系与带状图之间的对偶性。然后用Jenkins-Strebel微分和双曲几何两种不同的方法对曲线的模空间进行了纤维素化。我们还简要讨论了这两种方法是如何联系起来的。接下来，我们回顾Witten圈的定义，并说明它们与重言类和Weil-Petersson几何的联系。最后，我们给出了一个简单的直接论证来证明Witten类是稳定的。
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英文标题：
《Riemann surfaces, ribbon graphs and combinatorial classes》
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作者：
Gabriele Mondello
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最新提交年份：
2007
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分类信息：

一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics        数学
二级分类：Differential Geometry        微分几何
分类描述：Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis
复形，接触，黎曼，伪黎曼和Finsler几何，相对论，规范理论，整体分析
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英文摘要：
  This survey paper begins with the description of the duality between arc systems and ribbon graphs embedded in a punctured surface. Then we explain how to cellularize the moduli space of curves in two different ways: using Jenkins-Strebel differentials and using hyperbolic geometry. We also briefly discuss how these two methods are related. Next, we recall the definition of Witten cycles and we illustrate their connection with tautological classes and Weil-Petersson geometry. Finally, we exhibit a simple direct argument to prove that Witten classes are stable.
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PDF链接：
https://arxiv.org/pdf/0705.1792