On the homotopy type of the Deligne-Mumford compactification

Abstract

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.

14 pages, published version

References in corpus (1)

• Etale homotopy types of moduli stacks of algebraic curves with symmetries

Cited by in corpus (1)

• The stratified homotopy type of the reductive Borel-Serre compactification