Skip to main content
eScholarship
Open Access Publications from the University of California

Actions of Lie groups and Lie algebras on manifolds

  • Author(s): Hirsch, Morris W
  • et al.
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.

Many UC-authored scholarly publications are freely available on this site because of the UC Academic Senate's Open Access Policy. Let us know how this access is important for you.

Main Content
Current View