Symmetrized topological complexity

Mark Grant (Corresponding Author)

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Abstract

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
Volume11
Issue number2
Early online date5 Oct 2017
DOIs
Publication statusPublished - 1 Jun 2019

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology

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