The Barratt--Priddy--Quillen theorem via scanning methods
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910002812289024 |
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| author | Delarue, Marie-Camille |
| author_facet | Delarue, Marie-Camille |
| contents | The homology of the symmetric groups stabilizes, and the Barratt--Priddy--Quillen theorem identifies the stable homology with that of the infinite loop space underlying the sphere spectrum.
We formulate a new proof inspired by Galatius, Kupers, and Randal-Williams using scanning methods.
We build a topological model for the monoid formed by all the symmetric groups as a category of paths in $\mathbb{R}^\infty$ and build a scanning map from this model to a space of local images. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_13564 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Barratt--Priddy--Quillen theorem via scanning methods Delarue, Marie-Camille Algebraic Topology The homology of the symmetric groups stabilizes, and the Barratt--Priddy--Quillen theorem identifies the stable homology with that of the infinite loop space underlying the sphere spectrum. We formulate a new proof inspired by Galatius, Kupers, and Randal-Williams using scanning methods. We build a topological model for the monoid formed by all the symmetric groups as a category of paths in $\mathbb{R}^\infty$ and build a scanning map from this model to a space of local images. |
| title | The Barratt--Priddy--Quillen theorem via scanning methods |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2510.13564 |