Spaces of topological complexity one

Mark Grant*, Gregory Lupton, John Oprea

*Corresponding author for this work

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

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
Volume15
Issue number2
DOIs
Publication statusPublished - 2013

Keywords

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

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