Algebraic & Geometric Topology 8 (2008) 2049–2062

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.

Keywords

Deligne–Mumford compactification, moduli of curves, stack, mapping class group, orbit category

Mathematical Subject Classification

Primary: 32G15

Secondary: 14A20, 14D22, 30F60

References

Publication

Received: 16 July 2008
Accepted: 24 September 2008
Published: 5 November 2008

Authors