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arXiv · 2207.05026

Classical homological stability from the point of view of cells

Oscar Randal-Williams
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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.

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BibTeXRIS

Oscar Randal-Williams. 2022-07-11. Classical homological stability from the point of view of cells. https://doi.org/10.2140/agt.2024.24.1691

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