曲线模空间的非交换几何与紧化
Noncommutative geometry and compactifications of the moduli space of curves
摘要：
本文证明了Kontsevich在研究Witten代数时引入的模空间的某种自然紧化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.这个双参数族是通过使用非交换0-形式空间上的Lie余括号来构造的，这种结构对应于Riemann曲面上的Pinching简单闭曲线，以变形Kontsevich在随后的论文中描述的非交换辛几何。
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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