Abstract
Abstract In this paper we prove that every proper Lie groupoid admits a regularization to a regular proper Lie groupoid. When equipped with a Riemannian metric, we show that it admits regularization to a regular Riemannian proper Lie groupoid, arbitrarily close to the original one in the Gromov–Hausdorff distance between the quotient spaces. We construct the regularization via a successive blow-up construction on a proper Lie groupoid. We also prove that our construction of the regularization is invariant under Morita equivalence of groupoids, showing that it is a desingularization of the underlying differentiable stack.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
