Topological complexity, fibrations and symmetry

Mark Grant

Published 2011-04-14, updated 2011-09-26Version 4

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.