Spaces of topological complexity one

Mark Grant; Gregory Lupton; John Oprea

doi:10.4310/HHA.2013.v15.n2.a4

Spaces of topological complexity one

Mark Grant
, Gregory Lupton
, John Oprea

The University of Nottingham
Cleveland State University

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

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 TCn(X) is as low as possible, namely n - 1. © 2013, International Press.

Original language	English
Pages (from-to)	73-81
Number of pages	9
Journal	Homology, Homotopy and Applications
Volume	15
Issue number	2
DOIs	https://doi.org/10.4310/HHA.2013.v15.n2.a4
State	Published - Sep 19 2013

Keywords

Acyclic space
Co-H-space
Homology sphere
Lusternik-Schnirelmann category
Topological complexity
Topological robotics

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10.4310/HHA.2013.v15.n2.a4

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KW - Topological robotics

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Spaces of topological complexity one

Abstract

Keywords

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