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Actions of Lie groups and Lie algebras on manifolds
Abstract
Questions of the following sort are addressed:
Does a given Lie group or Lie algebra act effectively on a given manifold? How smooth can such actions be? What fixed point sets are possible? What happens under perturbations?
Old results are summarized and new ones presented, including: For every integer n there are solvable (in some cases, nilpotent) Lie algebras g that have effective smooth actions on all n-manifolds, but on some (in many cases, all) n-manifolds, g does not have effective analytic actions.
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