The Barratt--Priddy--Quillen theorem via scanning methods
Authors
Marie-Camille Delarue
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.
