Parametrised topological complexity of group epimorphisms

Mark Grant* (Corresponding Author)

*Corresponding author for this work

Research output: Working paper

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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.
Original languageEnglish
PublisherArXiv
Publication statusPublished - 4 Jun 2021

Keywords

  • parametrised topological complexity
  • aspherical spaces
  • group epimorphisms

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