Geometry & Topology

Madsen–Weiss for geometrically minded topologists

Yakov Eliashberg, Søren Galatius, and Nikolai Mishachev

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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.

Article information

Geom. Topol., Volume 15, Number 1 (2011), 411-472.

Received: 3 August 2009
Revised: 4 December 2010
Accepted: 5 January 2011
First available in Project Euclid: 20 December 2017

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Madsen–Weiss theorem Mumford conjecture Harer stability theorem


Eliashberg, Yakov; Galatius, Søren; Mishachev, Nikolai. Madsen–Weiss for geometrically minded topologists. Geom. Topol. 15 (2011), no. 1, 411--472. doi:10.2140/gt.2011.15.411.

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