Invariant topological complexity

lubawski, wojciech; marzantowicz, waclaw;

We present a new approach to an equivariant version of Farber’s topological complexity called
invariant topological complexity. It seems that the presented approach is more adequate for the
analysis of impact of a symmetry on a motion planning algorithm than the one introduced and
studied by Colman and Grant. We show many bounds for the invariant topological complexity
comparing it with already known invariants and prove that in the case of a free action it is equal
to the topological complexity of the orbit space. We define the Whitehead version of it.