  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
