Linearization Problems for Lie Algebroids and Lie Groupoids

Details Linearization Problems for Lie Algebroids and Lie Groupoids Linearization Problems for Lie Algebroids and Lie Groupoids

1999-12-22

arxiv.org/abs/math/9912189v1

Lett. Math. Phys. 52 (2000), 93-102.

Mathematics

Differential Geometry

In memory of Moshe Flato; 12 pages

Scientific paper

In this survey, we discuss a series of linearization problems--for Poisson structures, Lie algebroids, and Lie groupoids. The last problem involves a conjecture on the structure of proper groupoids. Attempting to prove this by the method of averaging leads to problems concerning almost actions of compact groups and almost invariant submanifolds for compact group actions. The paper ends with a discussion of possible extensions of the convexity theorems for momentum maps of hamiltonian actions of compact groups.

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