Classical homological stability from the point of view of cells
arXiv:2207.05026 · doi:10.2140/agt.2024.24.1691
Abstract
We explain how to interpret the complexes arising in the "classical" homology stability argument (e.g. in the framework of Randal-Williams--Wahl) in terms of higher algebra, which leads to a new proof of homological stability in this setting. The key ingredient is a theorem of Damiolini on the contractibility of certain arc complexes. We also explain how to directly compare the connectivities of these complexes with that of the "splitting complexes" of Galatius--Kupers--Randal-Williams.
13 pages; v2. 19 pages, accepted version to appear in Algebraic & Geometric Topology