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On the stable cohomology of the automorphism groups of free groups with coefficients
Multi angle
Authors : Vespa, Christine (Author of the conference)
CIRM (Publisher )
18D10 - Monoidal, symmetric monoidal and braided categories
20F28 - Automorphism groups of groups, See also {20E36}
20J06 - Cohomology of finite groups
CIRM (Publisher )
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Abstract :
In this talk, I will give an overview of known results on the stable cohomology of the automorphism groups of free groups with twisted coefficients. After explaining the notion of wheeled PROPs, I will describe a wheeled PROP structure on the stable cohomology of automorphism groups of free groups with some particular coefficients. I will explain how cohomology classes, constructed previously by Kawazumi, can be interpreted using this wheeled PROP structure and I will construct a morphism of wheeled PROPs from a PROP given in terms of functor homology and the wheeled PROP evoked previously. This is joint work with Nariya Kawazumi.
Keywords : Stable cohomology; automorphism groups; wheeled PROP
MSC Codes : Keywords : Stable cohomology; automorphism groups; wheeled PROP
18D10 - Monoidal, symmetric monoidal and braided categories
20F28 - Automorphism groups of groups, See also {20E36}
20J06 - Cohomology of finite groups
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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 ; Geometric Topology Mathematical Area(s) : Algebra ; Topology Format : MP4 (.mp4) - HD Video Time : 01:12:04 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-01-26-vespa.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.19998603Cite this video as: Vespa, Christine (2023). On the stable cohomology of the automorphism groups of free groups with coefficients. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19998603 URI : http://dx.doi.org/10.24350/CIRM.V.19998603 |
See Also
- [Multi angle] Coinvariants, assembler K-theory, and scissors congruence / Author of the conference Zakharevich, Inna.
- [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] (2)-categorical constructions and the multiplicative equivariant Barratt- Quillen-Priddy theorem / Author of the conference Osorno, Angélica.
- [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
- KAWAZUMI, Nariya et VESPA, Christine. On the wheeled PROP of stable cohomology of Aut (F_n) with bivariant coefficients. arXiv preprint arXiv:2105.14497, 2021 (To be published in Algebraic and Geometric Topology) - https://arxiv.org/abs/2105.14497
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