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We observe that any connected proper Lie groupoid whose orbits havecodimension at most two admits a globally effective representation on a smoothvector bundle, i.e., one whose kernel consists only of ineffective arrows. Asan application, we deduce that any such groupoid can up to Morita equivalencebe presented as an extension of some action groupoid G n X with G compact bysome bundle of compact Lie groups.

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