Symmetrized topological complexity

Mark Grant* (Corresponding Author)

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
20 Downloads (Pure)


We present upper and lower bounds for symmetrized topological complexity TCΣ(X) in the sense of Basabe–Gonzalez–Rudyak–Tamaki. The upper bound comes from equivariant obstruction theory, and the lower bounds from the cohomology of the symmetric square SP2 (X). We also show that symmetrized topological complexity coincides with its monoidal version, where the path from a point to itself is required to be constant. Using these results, we calculate the symmetrized topological complexity of all odd spheres.
Original languageEnglish
Pages (from-to)387-403
Number of pages17
JournalJournal of Topology and Analysis
Issue number2
Early online date5 Oct 2017
Publication statusPublished - 1 Jun 2019


  • Topological complexity
  • topological robotics
  • equivariant homotopy theory
  • symmetric products


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