Madsen-Weiss for geometrically minded topologists

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Eliashberg, Yakov
Galatius, Soren
Mishachev, Nikolai
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Abstract
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We give an alternative proof of Madsen-Weiss' generalized Mumford conjecture. Our proof is based on ideas similar to Madsen-Weiss' original proof, but it is more geometrical and less homotopy theoretical in nature. At the heart of the argument is a geometric version of Harer stability, which we formulate as a theorem about folded maps.
Comment: 67 pages, 15 figures
Keywords
Mathematics - Geometric Topology, Mathematics - Algebraic Topology, 57R45, 14H15
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