Parametrised topological complexity of group epimorphisms
Algebraic Topology
2021-10-28 v2 Group Theory
Abstract
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.
Cite
@article{arxiv.2106.02667,
title = {Parametrised topological complexity of group epimorphisms},
author = {Mark Grant},
journal= {arXiv preprint arXiv:2106.02667},
year = {2021}
}
Comments
v2: Final version, to appear in Topol. Methods Nonlinear Anal. Removed Lemma 2.3, whose proof contained a gap, and replaced with a reference