Séminaires : Séminaire d'Algèbres d'Opérateurs

Equipe(s) : ao,
Responsables :Pierre Fima, François Le Maître, Romain Tessera
Email des responsables :
Salle : 1013
Adresse :Sophie Germain

Orateur(s) Clément Dell'Aiera - ENS de Lyon,
Titre Dynamic asymptotic dimension and homology
Horaire14:00 à 15:00
Diffusion https://bigbluebutton3.imj-prg.fr/b/fra-j6k-9fw/
RésumeGroupoid homology has attracted increasing attention from the topological dynamics and operator algebras communities following the work of Matui. Matui's HK conjecture predicts that the K-theory groups of the reduced C*-algebra of a minimal essentially principal ample groupoid coincides with its homology groups. We prove that homology of principal ample groupoids vanishes in degree above its dynamical asymptotic dimension, a notion of dimension from topological dynamics. We deduce several consequences: Matui's HK conjecture holds for low dimensional principal ample groupoids, and classification of their reduced C*-algebra. (Joint work with Christian Bonicke, Jamie Gabe and Rufus Willett)
AdresseSophie Germain