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

Date: 2022-04-14

Time: 14:15 - 16:00


Nathalie Wahl


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.