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2008 On the homotopy type of the Deligne–Mumford compactification
Johannes Ebert, Jeffrey Giansiracusa
Algebr. Geom. Topol. 8(4): 2049-2062 (2008). DOI: 10.2140/agt.2008.8.2049

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 étale 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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Johannes Ebert. Jeffrey Giansiracusa. "On the homotopy type of the Deligne–Mumford compactification." Algebr. Geom. Topol. 8 (4) 2049 - 2062, 2008. https://doi.org/10.2140/agt.2008.8.2049

Information

Received: 16 July 2008; Accepted: 24 September 2008; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1160.32015
MathSciNet: MR2452916
Digital Object Identifier: 10.2140/agt.2008.8.2049

Subjects:
Primary: 32G15
Secondary: 14A20, 14D22, 30F60

Rights: Copyright © 2008 Mathematical Sciences Publishers

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