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arXiv · 1706.07843

Resolutions of proper Riemannian Lie groupoids

Hessel B. Posthuma·Xiang Tang·Kirsten J. L. Wang
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Abstract

In this paper we prove that every proper Lie groupoid admits a desingularization to a regular proper Lie groupoid. When equipped with a Riemannian metric, we show that it admits a desingularization 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 desingularization via a successive blow-up construction on a proper Lie groupoid. We also prove that our construction of the desingularization is invariant under Morita equivalence of groupoids, showing that it is a desingularization of the underlying differentiable stack.

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BibTeXRIS

Hessel B. Posthuma, Xiang Tang, Kirsten J. L. Wang. 2017-06-23. Resolutions of proper Riemannian Lie groupoids. https://arxiv.org/abs/1706.07843

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