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On the homotopy type of the Deligne–Mumford compactification
Algebraic & Geometric Topology, Volume: 8, Issue: 4, Pages: 2049 - 2062
Swansea University Author:
Jeffrey Giansiracusa
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DOI (Published version): 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...
| Published in: | Algebraic & Geometric Topology |
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| ISSN: | 1472-2739 1472-2747 |
| Published: |
Mathematical Sciences Publishers
2008
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| Online Access: |
Check full text
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa13607 |
| 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. |
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| College: |
Faculty of Science and Engineering |
| Issue: |
4 |
| Start Page: |
2049 |
| End Page: |
2062 |