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arXiv · 1207.4725

Spaces of Topological Complexity One

Mark Grant·Gregory Lupton·John Oprea
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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.

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Mark Grant, Gregory Lupton, John Oprea. 2012-07-19. Spaces of Topological Complexity One. https://arxiv.org/abs/1207.4725

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