The Mumford conjecture, Madsen-Weiss and homological stability for mapping class groups of surfaces | Zendy

Nathalie Wahl | Zendy

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The Mumford conjecture, Madsen-Weiss and homological stability for mapping class groups of surfaces

Author(s) -

Nathalie Wahl

Publication year - 2013

Publication title -

ias/park city mathematics series

Language(s) - English

Resource type - Book series

eISSN - 2472-5064

pISSN - 1079-5634

DOI - 10.1090/pcms/020/04

Subject(s) - conjecture , class (philosophy) , mathematics , mapping class group , pure mathematics , stability (learning theory) , algebra over a field , combinatorics , geometry , computer science , artificial intelligence , surface (topology) , machine learning

We give a complete and detailed proof of Harer's stability theorem for the homology of mapping class groups of surfaces, with the best stability range presently known. This theorem and its proof have seen several improvements since Harer's original proof in the mid-80's, and our purpose here is to assemble these many additions.

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