Homology of the open moduli space of curves

Ib Henning Madsen

doi:10.4171/103

Homology of the open moduli space of curves

Department of Mathematical Sciences

Abstract

This is a survey on the proof of a generalized version of the Mumford conjecture obtained in joint work with M. Weiss stating that a certain map between some classifying spaces which a priori have different natures induces an isomorphism at the level of integral homology. We also discuss our proof of the original Mumford conjecture stating that the stable rational cohomology of the moduli space of Riemann surfaces is a certain polynomial algebra generated by the Mumford–Morita–Miller cohomology classes of even degrees.

Original language	English
Title of host publication	Handbook of Teichmüller Theory
Editors	Athanase Papadopoulos
Volume	3
Publisher	European Mathematical Society
Publication date	2012
Pages	717–746
ISBN (Print)	978-3-03719-103-3
DOIs	https://doi.org/10.4171/103
Publication status	Published - 2012

Series	I R M A Lectures in Mathematics and Theoretical Physics
Volume	17

Access to Document

10.4171/103

Cite this

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