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.
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