Homology of the open moduli space of curves
Research output: Chapter in Book/Report/Conference proceeding › Book chapter › Research › peer-review
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Homology of the open moduli space of curves. / Madsen, Ib Henning.
Handbook of Teichmüller Theory. ed. / Athanase Papadopoulos. Vol. 3 European Mathematical Society, 2012. p. 717–746 (I R M A Lectures in Mathematics and Theoretical Physics, Vol. 17).Research output: Chapter in Book/Report/Conference proceeding › Book chapter › Research › peer-review
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TY - CHAP
T1 - Homology of the open moduli space of curves
AU - Madsen, Ib Henning
PY - 2012
Y1 - 2012
N2 - 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.
AB - 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.
U2 - 10.4171/103
DO - 10.4171/103
M3 - Book chapter
SN - 978-3-03719-103-3
VL - 3
T3 - I R M A Lectures in Mathematics and Theoretical Physics
SP - 717
EP - 746
BT - Handbook of Teichmüller Theory
A2 - Papadopoulos, Athanase
PB - European Mathematical Society
ER -
ID: 45172473