Volume 15, issue 1 (2011)

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Madsen–Weiss for geometrically minded topologists

Yakov Eliashberg, Søren Galatius and Nikolai Mishachev

Geometry & Topology 15 (2011) 411–472
Abstract

We give an alternative proof of the Madsen–Weiss generalized Mumford conjecture. At the heart of the argument is a geometric version of Harer stability, which we formulate as a theorem about folded maps. A technical ingredient in the proof is an $h$–principle type statement, called the “wrinkling theorem” by the first and third authors [Invent. Math. 130 (1997) 345–369]. Let us stress the point that we are neither proving the wrinkling theorem nor the Harer stability theorem.

 Dedicated to D B Fuchs on the occasion of his 70th birthday
Keywords
Madsen–Weiss theorem, Mumford conjecture, Harer stability theorem
Publication
Received: 3 August 2009
Revised: 4 December 2010
Accepted: 5 January 2011
Published: 11 March 2011
Proposed: Tom Mrowka
Seconded: Ralph Cohen, Peter Ozsváth
Authors
 Yakov Eliashberg Department of Mathematics Stanford University Building 380 Stanford CA 94305 USA Søren Galatius Department of Mathematics Stanford University Building 380 Stanford CA 94305 USA Nikolai Mishachev Department of Mathematics Lipetsk State Technical University 30 Moskovskaya St Lipetsk 398055 Russia