We show that the parametrised topological complexity of Cohen, Farber and Weinberger gives an invariant of group epimorphisms. We extend various bounds for the topological complexity of groups to obtain bounds for the parametrised topological complexity of epimorphisms. Several applications are given, including an alternative computation of the parametrised topological complexity of the planar Fadell--Neuwirth fibrations which avoids calculations involving cup products. We also prove a homotopy invariance result for parametrised topological complexity of fibrations over different bases.
- Pub Date:
- June 2021
- Mathematics - Algebraic Topology;
- Mathematics - Group Theory;
- 55M30 (Primary);
- 20J06 (Secondary)
- v2: Final version, to appear in Topol. Methods Nonlinear Anal. Removed Lemma 2.3, whose proof contained a gap, and replaced with a reference