Geometry of orbit spaces of proper Lie groupoids

By Markus J. Pflaum, H. Posthuma, X. Tang. 2010

62 citations recorded by the source corpus.

In this paper, we study geometric properties of quotient spaces of proper Lie groupoids. First, we construct a natural stratification on such spaces using an extension of the slice theorem for proper Lie groupoids of Weinstein and Zung. Next, we show the existence of an appropriate metric on the groupoid which gives the associated Lie algebroid the structure of a singular riemannian foliation. With this metric, the orbit space inherits a natural length space structure whose properties are studied. Moreover, we show that the orbit space of a proper Lie groupoid can be triangulated. Finally, we prove a de Rham theorem for the complex of basic differential forms on a proper Lie groupoid.

Subfields: Algebra and Number Theory, Mathematical Physics, Pathology and Forensic Medicine

View Paper: https://www.semanticscholar.org/paper/f98f74d5a6e5b78fc0a7a70a387b18ceedda0d32

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In Algebra and Number Theory

In Mathematical Physics

In Pathology and Forensic Medicine

Citations in the corpus

Riemannian metrics on Lie groupoids (2014, background): “Such metrics and their properties have been studied in [16].”