We show how locally smooth actions of compact Lie groups on a manifold X can be used to obtain new upper bounds for the topological complexity TC(X), in the sense of Farber. We also obtain new bounds for the topological complexity of finitely generated torsion-free nilpotent groups. (C) 2011 Elsevier B.V. All rights reserved.
Bibliographical noteAcknowledgements The author would like to thank John Oprea and Greg Lupton for stimulating discussions, and Michael Farber, Peter Landweber and the anonymous referee for their comments on earlier drafts of the paper.
- topological complexity
- transformation groups
- Lusternik-Schnirelmann category
- robot motion