摘要翻译：
本文研究了具有$N$标记点的$G$属热带曲线模空间的拓扑。我们把模空间看作嵌入在一个更大的空间中，我们称之为具有$n$标记点的度量图的{\it模空间。}我们描述了收缩桥梁的强变形收缩，这导致了所有这些模空间的实质性简化。在本文的其余部分，我们用这个约简来分析1属的情形。相应的模空间表示为环面关于共轭${\mathbb Z}_2$作用的商空间；此外，作为一个简单图上的同伦colimit。后者允许我们计算系数为${\mathbb Z}_2$的模空间的所有Betti数。
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英文标题：
《Topology of moduli spaces of tropical curves with marked points》
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作者：
Dmitry N. Kozlov
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最新提交年份：
2008
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分类信息：

一级分类：Mathematics        数学
二级分类：Algebraic Topology        代数拓扑
分类描述：Homotopy theory, homological algebra, algebraic treatments of manifolds
同伦理论，同调代数，流形的代数处理
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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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英文摘要：
  In this paper we study topology of moduli spaces of tropical curves of genus $g$ with $n$ marked points. We view the moduli spaces as being imbedded in a larger space, which we call the {\it moduli space of metric graphs with $n$ marked points.} We describe the shrinking bridges strong deformation retraction, which leads to a substantial simplification of all these moduli spaces. In the rest of the paper, that reduction is used to analyze the case of genus 1. The corresponding moduli space is presented as a quotient space of a torus with respect to the conjugation ${\mathbb Z}_2$-action; and furthermore, as a homotopy colimit over a simple diagram. The latter allows us to compute all Betti numbers of that moduli space with coefficients in ${\mathbb Z}_2$.
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PDF链接：
https://arxiv.org/pdf/0809.4357