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
Cite
@article{arxiv.1204.1689,
title = {Actions of Lie groups and Lie algebras on manifolds},
author = {Morris W. Hirsch},
journal= {arXiv preprint arXiv:1204.1689},
year = {2012}
}
Comments
A Celebration of the Mathematical Legacy of Raoul Bott, 69-78. Centre de Recherches Math\'ematiques, U. de Montr\'eal. Published in Proceedings & Lecture Notes Vol. 50, (P. R. Kotiuga, ed.), Amer. Math. Soc. Providence RI 2010. ISBN: 978-0-8218-4777-0