Spaces of topological complexity one

Mark Grant*, Gregory Lupton, John Oprea

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


We prove that a space whose topological complexity equals 1 is homotopy equivalent to some odd-dimensional sphere. We prove a similar result, although not in complete generality, for spaces X whose higher topological complexity TCn (X) is as low as possible, namely n - 1.

Original languageEnglish
Pages (from-to)73-81
Number of pages9
JournalHomology, Homotopy and Applications
Issue number2
Publication statusPublished - 2013


  • Lusternik-Schnirelmann category
  • topological complexity
  • topological robotics
  • acyclic space
  • co-H-space
  • homology sphere


Dive into the research topics of 'Spaces of topological complexity one'. Together they form a unique fingerprint.

Cite this