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Classical homological stability from the point of view of cells

Accepted version
Peer-reviewed

Type

Article

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Authors

Randal-Williams, Oscar  ORCID logo  https://orcid.org/0000-0002-7479-2878

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.

Description

Keywords

math.AT, math.AT, 55P48, 20J05

Journal Title

Algebr. Geom. Topol.

Conference Name

Journal ISSN

1472-2739

Volume Title

Publisher

Mathematical Sciences Publishers (MSP)

Publisher DOI