2022 Parametrised topological complexity of group epimorphisms
Mark Grant
Topol. Methods Nonlinear Anal. 60(1): 287-303 (2022). DOI: 10.12775/TMNA.2021.056

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.

Citation

Download Citation

Mark Grant. "Parametrised topological complexity of group epimorphisms." Topol. Methods Nonlinear Anal. 60 (1) 287 - 303, 2022. https://doi.org/10.12775/TMNA.2021.056

Information

Published: 2022
First available in Project Euclid: 8 September 2022

zbMATH: 1512.55005
MathSciNet: MR4524869
Digital Object Identifier: 10.12775/TMNA.2021.056

Keywords: aspherical space , group epimorphisms , Parametrised topological complexity

Rights: Copyright © 2022 Juliusz P. Schauder Centre for Nonlinear Studies

JOURNAL ARTICLE
17 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

Vol.60 • No. 1 • 2022
Back to Top