Linearization of proper groupoids

Details Linearization of proper groupoids Linearization of proper groupoids

2003-01-25

arxiv.org/abs/math/0301297v2

Mathematics

Differential Geometry

2nd version: some misprints corrected and some comments added

Scientific paper

We prove the following result, conjectured by Alan Weinstein: every smooth proper Lie groupoid near a fixed point is locally linearizable, i.e. it is locally isomorphic to the associated groupoid of a linear action of a compact Lie group. In combination with a slice theorem of Weinstein, our result implies the smooth linearizability of a proper Lie groupoid in the neighborhood of an orbit under a mild condition.

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