Effective topological complexity of spaces with symmetries

Abstract

We introduce a version of Farber's topological complexity suitable for investigating mechanical systems whose configuration spaces exhibit symmetries. Our invariant has vastly different properties to the previous approaches of Colman-Grant, Dranishnikov and Lubawski-Marzantowicz. In particular, it is bounded from above by Farber's topological complexity.

New title; a short section with open problems included at the end of the paper. Numerous minor improvements throughout the text. Final version, to appear in Publ. Mat. 19 pages, 2 figures