Madsen-Weiss for geometrically minded topologists
نویسندگان
چکیده
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.
منابع مشابه
The Mumford conjecture, Madsen-Weiss and homological stability for mapping class groups of surfaces
The Mumford conjecture, Madsen-Weiss and homological stability for mapping class groups of surfaces 3 Introduction 3 Lecture 1. The Mumford conjecture and the Madsen-Weiss theorem 5 1. The Mumford conjecture 5 2. Moduli space, mapping class groups and diffeomorphism groups 5 3. The Mumford-Morita-Miller classes 7 4. Homological stability 7 5. The Madsen-Weiss theorem 9 6. Exercices 10 Lecture 2...
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