Higher Algebra, Geometry, and Topology / Algèbre, Géométrie et Topologie Supérieures

Collection Higher Algebra, Geometry, and Topology / Algèbre, Géométrie et Topologie Supérieures

Organisateur(s) Campos, Ricardo ; Cirici, Joana ; Dotsenko, Vladimir ; Vallette, Bruno

Date(s) 06/05/2024 - 10/05/2024

URL associée https://conferences.cirm-math.fr/2995.html

00:00:00 / 00:00:00

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On analytic exponential functors on free groups

De Christine Vespa

Functors on the category gr of finitely generated free groups and group homomorphisms appear naturally in different contexts of topology. For example, Hochschild-Pirashvili homology for a wedge of circles or Jacobi diagrams in handlebodies give rise to interesting functors on gr. Some of these natural examples satisfy further properties: they are analytic and/or exponential. Pirashvili proves that the category of exponential contravariant functors from gr to the category k-Mod of k-modules is equivalent to the category of cocommutative Hopf algebras over k. Powell proves an equivalence between the category of analytic contravariant functors from gr to k-Mod, and the category of linear functors on the linear PROP associated to the Lie operad when k is a field of characteristic 0. In this talk, after explaining these two equivalences of categories, I will explain how they interact with each other. (This is a joint work with Minkyu Kim).

Informations sur la vidéo

Date de captation 07/05/2024
Date de publication 29/05/2024
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs, Doctorants
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.20173603
Citer cette vidéo Vespa, Christine (07/05/2024). On analytic exponential functors on free groups. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20173603
URL https://dx.doi.org/10.24350/CIRM.V.20173603

Domaine(s)

Topologie algébrique

Bibliographie

KIM, Minkyu et VESPA, Christine. On analytic exponential functors on free groups. arXiv preprint arXiv:2401.09151, 2024. - https://arxiv.org/abs/2401.09151

Codes MSC

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