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Madsen–Weiss for
geometrically minded topologists
Yakov Eliashberg, Søren Galatius and Nikolai Mishachev |
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Geometry & Topology 15 (2011) 411–472
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Abstract |
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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 –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. |
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Dedicated to D B Fuchs on the occasion of his 70th birthday |
Keywords
Madsen–Weiss theorem, Mumford conjecture, Harer stability
theorem
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References |
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
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Authors |
| Yakov Eliashberg | |
| Department of Mathematics Stanford University Building 380 Stanford CA 94305 USA |
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| Søren Galatius | |
| Department of Mathematics Stanford University Building 380 Stanford CA 94305 USA |
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| Nikolai Mishachev | |
| Department of Mathematics Lipetsk State Technical University 30 Moskovskaya St Lipetsk 398055 Russia |
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