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Nathalie Wahl: A new proof of best slope stability for the mapping class group of surfaces

Time: Thu 2022-04-14 14.15 - 16.00

Location: Institut Mittag-Leffler, Seminar Hall Kuskvillan and Zoom

Video link: Meeting ID: 921 756 1880

Participating: Nathalie Wahl (University of Copenhagen)

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Abstract: We use the "disordered arc complex" to give a quite direct proof of the slope 2/3 stability of the homology of the mapping class groups of surfaces, using Quillen's most standard spectral sequence argument for homological stability. This arc complex can be interpreted as a complex of destabilization for a certain disc-stabilization that has the effect of stabilizing "1/2 genus" at a time, and gives a rather exotic example of Krannich's stability framework for \(E_1\)-modules over \(E_2\)-algebras. This is joint work with Oscar Harr and Max Vistrup.