Volume 15, issue 3 (2015)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
A mapping theorem for topological complexity

Mark Grant, Gregory Lupton and John Oprea

Algebraic & Geometric Topology 15 (2015) 1643–1666
Abstract

We give new lower bounds for the (higher) topological complexity of a space in terms of the Lusternik–Schnirelmann category of a certain auxiliary space. We also give new lower bounds for the rational topological complexity of a space, and more generally for the rational sectional category of a map, in terms of the rational category of a certain auxiliary space. We use our results to deduce consequences for the global (rational) homotopy structure of simply connected hyperbolic finite complexes.

Keywords
Lusternik–Schnirelmann category, sectional category, topological complexity, topological robotics, sectioned fibration, connective cover, Avramov–Félix conjecture
Mathematical Subject Classification 2010
Primary: 55M30, 55P62
Secondary: 55S40, 55Q15
References
Publication
Received: 29 April 2014
Revised: 21 October 2014
Accepted: 23 October 2014
Published: 19 June 2015
Authors
Mark Grant
Institute of Pure and Applied Mathematics
University of Aberdeen
Fraser Noble Building
Aberdeen
AB24 3UE
UK
Gregory Lupton
Department of Mathematics
Cleveland State University
2121 Euclid Avenue
Cleveland, OH 44115
USA
John Oprea
Department of Mathematics
Cleveland State University
2121 Euclid Avenue
Cleveland, OH 44115
USA