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On the homotopy type of the Deligne–Mumford compactification / Johannes Ebert; Jeffrey Giansiracusa

Algebraic & Geometric Topology, Volume: 8, Issue: 4, Pages: 2049 - 2062

Swansea University Author: Giansiracusa, Jeffrey

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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...

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Published in: Algebraic & Geometric Topology
ISSN: 1472-2739 1472-2747
Published: Mathematical Sciences Publishers 2008
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa13607
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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.
College: College of Science
Issue: 4
Start Page: 2049
End Page: 2062