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(2)-categorical constructions and the multiplicative equivariant Barratt- Quillen-Priddy theorem
Multi angle
Authors : Osorno, Angélica (Author of the conference)
CIRM (Publisher )
19D23 - Symmetric monoidal categories, See also {18D10}
19L47 - Equivariant $K$-theory, See also {55N91, 55P91, 55Q91, 55R91, 55S91}
55P48 - Loop space machines, operads
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 : 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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Information on the Video
Film maker : Petit, JeanLanguage : 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 
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Information on the Event
Event Title : Chromatic Homotopy, K-Theory and Functors / Homotopie chromatique, K-théorie et foncteursEvent 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.19997903Cite 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
- [Multi angle] Coinvariants, assembler K-theory, and scissors congruence / Author of the conference Zakharevich, Inna.
- [Multi angle] On the stable cohomology of the automorphism groups of free groups with coefficients / Author of the conference Vespa, Christine.
- [Multi angle] Representation spheres and chromatic Picard groups / Author of the conference Stojanoska, Vesna.
- [Multi angle] How algebraic is a stable model category? / Author of the conference Roitzheim, Constanze.
- [Multi angle] Topological cyclic homology of the second truncated Brown–Peterson spectrum / Author of the conference Rognes, John.
- [Multi angle] Equivalences in higher categories / Author of the conference Ozornova, Viktoriya.
- [Multi angle] Equivariant homotopy theory for infinite groups and THH with coefficients / Author of the conference Nikolaus, Thomas.
- [Multi angle] Equivariant elliptic cohomology / Author of the conference Meier, Lennart.
- [Multi angle] The universal property of topological Hochschild homology / Author of the conference Harpaz, Yonatan.
- [Multi angle] Prismatic and syntomic cohomology of ring spectra / Author of the conference Hahn, Jeremy.
- [Multi angle] Spaces of quasi-invariants / Author of the conference Berest, Yuri.
- [Multi angle] A survey of Mackey and Green 2-functors / Author of the conference Dell'Ambrogio, Ivo.
- [Multi angle] The chromatic Nullstellensatz / Author of the conference Burklund, Robert.
- [Multi angle] Adjoining roots to ring spectra and algebraic K-theory / Author of the conference Bayindir, Haldun Özgür.
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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