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

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Authors : Osorno, Angélica (Author of the conference)
CIRM (Publisher )

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Abstract : 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.

Keywords : K-theory; multiplicative equivariant infinite loop spaces

MSC Codes :
19D23 - Symmetric monoidal categories, See also {18D10}
19L47 - Equivariant $K$-theory, See also {55N91, 55P91, 55Q91, 55R91, 55S91}
55P48 - Loop space machines, operads

    Information on the Video

    Film maker : Petit, Jean
    Language : English
    Available date : 17/02/2023
    Conference Date : 26/01/2023
    Subseries : Research talks
    arXiv category : Algebraic Topology
    Mathematical Area(s) : Topology
    Format : MP4 (.mp4) - HD
    Video Time : 00:59:20
    Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students
    Download : https://videos.cirm-math.fr/2023-01-26-osorno.mp4

Information on the Event

Event Title : Chromatic Homotopy, K-Theory and Functors / Homotopie chromatique, K-théorie et foncteurs
Event Organizers : Ausoni, Christian ; Hess Bellwald, Kathryn ; Powell, Geoffrey ; Touzé, Antoine ; Vespa, Christine
Dates : 23/01/2023 - 27/01/2023
Event Year : 2023
Event URL : https://conferences.cirm-math.fr/2339.html

Citation Data

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

See Also

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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