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2013 Spaces of topological complexity one
Mark Grant, Gregory Lupton, John Oprea
Homology Homotopy Appl. 15(2): 73-81 (2013).

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 $n-1$.

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Mark Grant. Gregory Lupton. John Oprea. "Spaces of topological complexity one." Homology Homotopy Appl. 15 (2) 73 - 81, 2013.

Information

Published: 2013
First available in Project Euclid: 8 November 2013

zbMATH: 1277.55001
MathSciNet: MR3117387

Subjects:
Primary: 55M30 , 55S40

Keywords: acyclic space , co-H-space , homology sphere , Lusternik-Schnirelmann category , topological complexity , topological robotics

Rights: Copyright © 2013 International Press of Boston

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Vol.15 • No. 2 • 2013
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