Deutsch Intern

Oberseminar Deformationsquantisierung und Geometrie: David Miyamoto (Max Planck Institut für Mathematik, Bonn)

Lie groupoids determined by their orbit spaces
Date: 02/09/2024, 2:00 PM - 3:30 PM
Category: Veranstaltung
Location: Hubland Nord, Geb. 30, SE30
Speaker: David Miyamoto (Max Planck Institut für Mathematik, Bonn)

Abstract: The orbit space of a Lie groupoid inherits a natural quotient diffeology. More generally, we have a quotient functor from the Hilsum-Skandalis category of Lie groupoids to the category of diffeological spaces. We introduce the notion of a lift-complete Lie groupoid, and show that the quotient functor restricts to an equivalence of the categories: of lift-complete Lie groupoids with isomorphism classes of submersive bibundles as arrows, and of quasi-étale diffeological spaces with local subductions as arrows. In particular, the Morita equivalence class of a lift-complete Lie groupoid is determined by its diffeological orbit space. Examples of lift-complete Lie groupoids include quasifold groupoids and étale holonomy groupoids of Riemannian foliations.