Chromatic Homotopy, K-Theory and Functors / Homotopie chromatique, K-théorie et foncteurs

Collection Chromatic Homotopy, K-Theory and Functors / Homotopie chromatique, K-théorie et foncteurs

Organizer(s) Ausoni, Christian ; Hess Bellwald, Kathryn ; Powell, Geoffrey ; Touzé, Antoine ; Vespa, Christine
Date(s) 23/01/2023 - 27/01/2023
linked URL https://conferences.cirm-math.fr/2339.html
00:00:00 / 00:00:00
12 15

(2)-categorical constructions and the multiplicative equivariant Barratt- Quillen-Priddy theorem

By Angélica Osorno

The classical Barratt-Priddy-Quillen theorem states that the $K$-theory spectrum of the category of finite sets and isomorphisms is equivalent to the sphere spectrum. A more general statement is that for an unbased space $X$, the suspension spectrum $\Sigma_{+}^{\infty} X$ is equivalent to the spectrum associated to the free $E_{\infty}$ space on $X$. In this talk we will present a categorical construction of the latter that is lax monoidal. This compatibility with multiplicative structures is necessary when using this functor to change enrichments, as in the work of Guillou-May.This is joint work with Bert Guillou, Peter May and Mona Merling.

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Citation data

  • DOI 10.24350/CIRM.V.19997903
  • Cite this video Osorno, Angélica (26/01/2023). (2)-categorical constructions and the multiplicative equivariant Barratt- Quillen-Priddy theorem. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19997903
  • URL https://dx.doi.org/10.24350/CIRM.V.19997903

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Bibliography

  • GUILLOU, Bertrand J., MAY, J. Peter, MERLING, Mona, et al. Multiplicative equivariant $ K $-theory and the Barratt-Priddy-Quillen theorem. arXiv preprint arXiv:2102.13246, 2021. To appear in Advances in Mathematics. - https://arxiv.org/abs/2102.13246

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