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 ${\sf TC}_n(X)$ is as low as possible, namely $n-1$.
Citation
Mark Grant. Gregory Lupton. John Oprea. "Spaces of topological complexity one." Homology Homotopy Appl. 15 (2) 73 - 81, 2013.
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