A note on the global structure of proper Lie groupoids in low codimensions

Details A note on the global structure of proper Lie groupoids in low codimensions A note on the global structure of proper Lie groupoids in low codimensions

2009-07-16

arxiv.org/abs/0907.2856v1

Topology Appl. 158 (5) (2011) pp. 708-717

Mathematics

Representation Theory

12 pages

Scientific paper

10.1016/j.topol.2011.01.019

We observe that any connected proper Lie groupoid whose orbits have codimension at most two admits a globally effective representation on a smooth vector bundle, i.e., one whose kernel consists only of ineffective arrows. As an application, we deduce that any such groupoid can up to Morita equivalence be presented as an extension of some action groupoid G n X with G compact by some bundle of compact Lie groups.

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