%0 Journal Article
%T Spaces of Topological Complexity One
%A Mark Grant
%A Gregory Lupton
%A John Oprea
%J Mathematics
%D 2012
%I arXiv
%X 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.
%U http://arxiv.org/abs/1207.4725v1