Resolutions of Proper Riemannian Lie Groupoids Article Swipe

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Mathematics Pure mathematics Double groupoid Quotient Lie group Equivalence (formal languages)

Hessel Posthuma , Xiang Tang , Kirsten J. L. Wang ·

YOU? · · 2018 · Open Access · · DOI: https://doi.org/10.1093/imrn/rny292 · OA: W2697234208

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.