Nguyen Tien Zung, Proper groupoids and momentum maps: linearization, affinity, and convexity. Ann. Sci. École Norm. Sup. (4) 39 (2006), no. 5, 841–869.
Preprint on arxiv: http://arxiv.org/abs/math/0407208
Paper at Science Direct: http://www.sciencedirect.com/science/article/pii/S0012959306000413
The main results of this paper are the following:
– Local smooth linearization theorem for proper Lie groupoids
– An analogous theorem for symplectic groupoids
– Abstract convexity results for momentum maps in the context of symplectic groupoid actions (which cover and generalize well-known convexity theorems in symplectic geometry)
The paper is dedicated to Alan Weinstein (who posed the question to me about linearization)
It was first sent to JAMS, got very good referee reports, but was rejected because one the the guys on the editorial board said that it “didn’t have enough applications” (?!). So I sent it to Annales ENS and it was quickly accepted there. I was flattered by Kirill Mackenzie who said that the local linearization result in this paper was among the most significant results in the theory of Lie groupoids.
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