摘要翻译：
本文证明了Kontsevich在研究Witten猜想时引入的模空间的某种自然紧致的同调可以完全代数地描述为某种微分分次李代数的同调。这个双参数族是利用非对易0-型空间上的一个李协括号构造的，它对应于黎曼曲面上简单闭曲线的捏缩，从而使Kontsevich在随后的论文中所描述的非对易辛几何变形。
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英文标题：
《Noncommutative geometry and compactifications of the moduli space of
  curves》
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作者：
Alastair Hamilton
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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：Quantum Algebra        量子代数
分类描述：Quantum groups, skein theories, operadic and diagrammatic algebra, quantum field theory
量子群，skein理论，运算代数和图解代数，量子场论
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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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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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英文摘要：
  In this paper we show that the homology of a certain natural compactification of the moduli space, introduced by Kontsevich in his study of Witten's conjectures, can be described completely algebraically as the homology of a certain differential graded Lie algebra. This two-parameter family is constructed by using a Lie cobracket on the space of noncommutative 0-forms, a structure which corresponds to pinching simple closed curves on a Riemann surface, to deform the noncommutative symplectic geometry described by Kontsevich in his subsequent papers.
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PDF链接：
https://arxiv.org/pdf/0710.4603