# 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

**Lecturer: **
Nathalie Wahl (University of Copenhagen)

**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.