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| Main Author: | |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2207.05026 |
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| _version_ | 1866914862865580032 |
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| author | Randal-Williams, Oscar |
| author_facet | Randal-Williams, Oscar |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_05026 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Classical homological stability from the point of view of cells Randal-Williams, Oscar Algebraic Topology 55P48, 20J05 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. |
| title | Classical homological stability from the point of view of cells |
| topic | Algebraic Topology 55P48, 20J05 |
| url | https://arxiv.org/abs/2207.05026 |