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On analytic exponential functors on free groups

By Christine Vespa

Appears in collection : Higher Algebra, Geometry, and Topology / Algèbre, Géométrie et Topologie Supérieures

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).

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  • DOI 10.24350/CIRM.V.20173603
  • Cite this video 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

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