Parametrised topological complexity of group epimorphisms

Mark Grant* (Corresponding Author)

*Corresponding author for this work

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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
Pages (from-to)287-303
Number of pages17
JournalTopological Methods in Nonlinear Analysis
Issue number1
Publication statusPublished - 31 Aug 2022


  • parametrised topological complexity
  • aspherical spaces
  • group epimorphisms


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