The Mumford conjecture

Geoffrey Powell

Séminaire Bourbaki (2004-2005)

  • Volume: 47, page 247-282
  • ISSN: 0303-1179

Abstract

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The Mumford Conjecture asserts that the rational cohomology of the stable moduli space of Riemann surfaces is a polynomial algebra on the Mumford-Morita-Miller characteristic classes; this can be reformulated in terms of the classifying space B Γ ∞ derived from the mapping class groups. The conjecture admits a topological generalization, inspired by Tillmann’s theorem that B Γ ∞ admits an infinite loop space structure after applying Quillen’s plus construction. The text presents the proof by Madsen and Weiss of the generalized Mumford conjecture.

How to cite

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Powell, Geoffrey. "The Mumford conjecture." Séminaire Bourbaki 47 (2004-2005): 247-282. <http://eudml.org/doc/252169>.

@article{Powell2004-2005,
abstract = {The Mumford Conjecture asserts that the rational cohomology of the stable moduli space of Riemann surfaces is a polynomial algebra on the Mumford-Morita-Miller characteristic classes; this can be reformulated in terms of the classifying space $B \Gamma _\infty $ derived from the mapping class groups. The conjecture admits a topological generalization, inspired by Tillmann’s theorem that $B \Gamma _\infty $ admits an infinite loop space structure after applying Quillen’s plus construction. The text presents the proof by Madsen and Weiss of the generalized Mumford conjecture.},
author = {Powell, Geoffrey},
journal = {Séminaire Bourbaki},
keywords = {conjecture de Mumford; espace de modules des courbes; groupe modulaire de Teichmüller; théorie de Morse; stratification},
language = {eng},
pages = {247-282},
publisher = {Association des amis de Nicolas Bourbaki, Société mathématique de France},
title = {The Mumford conjecture},
url = {http://eudml.org/doc/252169},
volume = {47},
year = {2004-2005},
}

TY - JOUR
AU - Powell, Geoffrey
TI - The Mumford conjecture
JO - Séminaire Bourbaki
PY - 2004-2005
PB - Association des amis de Nicolas Bourbaki, Société mathématique de France
VL - 47
SP - 247
EP - 282
AB - The Mumford Conjecture asserts that the rational cohomology of the stable moduli space of Riemann surfaces is a polynomial algebra on the Mumford-Morita-Miller characteristic classes; this can be reformulated in terms of the classifying space $B \Gamma _\infty $ derived from the mapping class groups. The conjecture admits a topological generalization, inspired by Tillmann’s theorem that $B \Gamma _\infty $ admits an infinite loop space structure after applying Quillen’s plus construction. The text presents the proof by Madsen and Weiss of the generalized Mumford conjecture.
LA - eng
KW - conjecture de Mumford; espace de modules des courbes; groupe modulaire de Teichmüller; théorie de Morse; stratification
UR - http://eudml.org/doc/252169
ER -

References

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