English
(2)-categorical constructions and the multiplicative equivariant Barratt- Quillen-Priddy theorem
Multi angle
Auteurs : Osorno, Angélica (Auteur de la Conférence)
CIRM (Editeur )
19D23 - Symmetric monoidal categories, See also {18D10}
19L47 - Equivariant $K$-theory, See also {55N91, 55P91, 55Q91, 55R91, 55S91}
55P48 - Loop space machines, operads
CIRM (Editeur )
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Résumé :
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
Codes MSC : Keywords : K-theory; multiplicative equivariant infinite loop spaces
19D23 - Symmetric monoidal categories, See also {18D10}
19L47 - Equivariant $K$-theory, See also {55N91, 55P91, 55Q91, 55R91, 55S91}
55P48 - Loop space machines, operads
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Informations sur la Vidéo
Réalisateur : Petit, JeanLangue : Anglais Date de publication : 17/02/2023 Date de captation : 26/01/2023 Sous collection : Research talks arXiv category : Algebraic Topology Domaine : Topology Format : MP4 (.mp4) - HD Durée : 00:59:20 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-01-26-osorno.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Chromatic Homotopy, K-Theory and Functors / Homotopie chromatique, K-théorie et foncteursOrganisateurs de la rencontre : Ausoni, Christian ; Hess Bellwald, Kathryn ; Powell, Geoffrey ; Touzé, Antoine ; Vespa, Christine Dates : 23/01/2023 - 27/01/2023 Année de la rencontre : 2023 URL Congrès : https://conferences.cirm-math.fr/2339.html
Données de citation
DOI : 10.24350/CIRM.V.19997903Citer cette vidéo: 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 |
Voir aussi
- [Multi angle] Coinvariants, assembler K-theory, and scissors congruence / Auteur de la Conférence Zakharevich, Inna.
- [Multi angle] On the stable cohomology of the automorphism groups of free groups with coefficients / Auteur de la Conférence Vespa, Christine.
- [Multi angle] Representation spheres and chromatic Picard groups / Auteur de la Conférence Stojanoska, Vesna.
- [Multi angle] How algebraic is a stable model category? / Auteur de la Conférence Roitzheim, Constanze.
- [Multi angle] Topological cyclic homology of the second truncated Brown–Peterson spectrum / Auteur de la Conférence Rognes, John.
- [Multi angle] Equivalences in higher categories / Auteur de la Conférence Ozornova, Viktoriya.
- [Multi angle] Equivariant homotopy theory for infinite groups and THH with coefficients / Auteur de la Conférence Nikolaus, Thomas.
- [Multi angle] Equivariant elliptic cohomology / Auteur de la Conférence Meier, Lennart.
- [Multi angle] The universal property of topological Hochschild homology / Auteur de la Conférence Harpaz, Yonatan.
- [Multi angle] Prismatic and syntomic cohomology of ring spectra / Auteur de la Conférence Hahn, Jeremy.
- [Multi angle] Spaces of quasi-invariants / Auteur de la Conférence Berest, Yuri.
- [Multi angle] A survey of Mackey and Green 2-functors / Auteur de la Conférence Dell'Ambrogio, Ivo.
- [Multi angle] The chromatic Nullstellensatz / Auteur de la Conférence Burklund, Robert.
- [Multi angle] Adjoining roots to ring spectra and algebraic K-theory / Auteur de la Conférence Bayindir, Haldun Özgür.
Bibliographie
- 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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