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 fxed-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 C-infinity actions on all n-manifolds, but on some (in many cases, all) n-manifolds, g does not have effective analytic actions