Parametrised topological complexity of group epimorphisms
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Publication:6369486
DOI10.12775/TMNA.2021.056arXiv2106.02667MaRDI QIDQ6369486
Publication date: 4 June 2021
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.
Lyusternik-Shnirel'man category of a space, topological complexity à la Farber, topological robotics (topological aspects) (55M30) Cohomology of groups (20J06) Eilenberg-Mac Lane spaces (55P20)
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