Parametrised topological complexity of group epimorphisms
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 FadellNeuwirth fibrations which avoids calculations involving cup products. We also prove a homotopy invariance result for parametrised topological complexity of fibrations over different bases.
 Publication:

arXiv eprints
 Pub Date:
 June 2021
 DOI:
 10.48550/arXiv.2106.02667
 arXiv:
 arXiv:2106.02667
 Bibcode:
 2021arXiv210602667G
 Keywords:

 Mathematics  Algebraic Topology;
 Mathematics  Group Theory;
 55M30 (Primary);
 55P20;
 20J06 (Secondary)
 EPrint:
 v2: Final version, to appear in Topol. Methods Nonlinear Anal. Removed Lemma 2.3, whose proof contained a gap, and replaced with a reference