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arXiv · 2510.13564

The Barratt--Priddy--Quillen theorem via scanning methods

Marie-Camille Delarue
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Abstract

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.

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Marie-Camille Delarue. 2025-10-15. The Barratt--Priddy--Quillen theorem via scanning methods. https://arxiv.org/abs/2510.13564

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