English

Spaces of Topological Complexity One

Algebraic Topology 2012-07-20 v1

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 TC_n(X) is as low as possible, namely n-1.

Keywords

Cite

@article{arxiv.1207.4725,
  title  = {Spaces of Topological Complexity One},
  author = {Mark Grant and Gregory Lupton and John Oprea},
  journal= {arXiv preprint arXiv:1207.4725},
  year   = {2012}
}

Comments

9 pages

R2 v1 2026-06-21T21:38:35.967Z