Effectual topological complexity

We introduce the effectual topological complexity (ETC) of a [Formula: see text]-space text]. This is text]-equivariant homotopy invariant sitting in between effective pair text] and (regular) orbit space study ETC for spheres surfaces with antipodal involution, obtaining full computation case torus. allows us to prove vanishing twice nontrivial obstruction responsible fact that Klein bottle In addition, this gives counterexample possibility — suggested Pavešić’s work on map would agree Farber’s whenever projection finitely sheeted. conjecture action recasts Hopf one problem, describe (conjecturally optimal) motion planners.