Homology, Homotopy and Applications
Volume 15 (2013)
Spaces of topological complexity one
Pages: 73 – 81
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 $n - 1$.
Lusternik-Schnirelmann category, topological complexity, topological robotics, acyclic space, co-H-space, homology sphere
2010 Mathematics Subject Classification