Actions of Lie groups and Lie algebras on manifolds

Details Actions of Lie groups and Lie algebras on manifolds Actions of Lie groups and Lie algebras on manifolds

2012-04-07

arxiv.org/abs/1204.1689v1

Mathematics

Group Theory

A Celebration of the Mathematical Legacy of Raoul Bott, 69-78. Centre de Recherches Math\'ematiques, U. de Montr\'eal. Publish

Scientific paper

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

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