arXiv 0807.25762008-07math.ATmath.AG

On the homotopy type of the Deligne-Mumford compactification

Johannes Ebert, Jeffrey Giansiracusa

备注：: 14 pages, published version
发表信息：: Algebr. Geom. Topol. 8 (2008) 2049-2062
DOI：: 10.2140/agt.2008.8.2049

英文摘要：

An old theorem of Charney and Lee says that the classifying space of the category of stable nodal topological surfaces and isotopy classes of degenerations has the same rational homology as the Deligne-Mumford compactification. We give an integral refinement: the classifying space of the Charney-Lee category actually has the same homotopy type as the moduli stack of stable curves, and the etale homotopy type of the moduli stack is equivalent to the profinite completion of the classifying space of the Charney-Lee category.

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