Algebraic & Geometric Topology

A mapping theorem for topological complexity

Mark Grant, Gregory Lupton, and John Oprea

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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.

Article information

Source
Algebr. Geom. Topol., Volume 15, Number 3 (2015), 1643-1666.

Dates
Received: 29 April 2014
Revised: 21 October 2014
Accepted: 23 October 2014
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1510840970

Digital Object Identifier
doi:10.2140/agt.2015.15.1643

Mathematical Reviews number (MathSciNet)
MR3361146

Zentralblatt MATH identifier
1321.55002

Subjects
Primary: 55M30: Ljusternik-Schnirelman (Lyusternik-Shnirelʹman) category of a space 55P62: Rational homotopy theory
Secondary: 55S40: Sectioning fiber spaces and bundles 55Q15: Whitehead products and generalizations

Keywords
Lusternik–Schnirelmann category sectional category topological complexity topological robotics sectioned fibration connective cover Avramov–Félix conjecture

Citation

Grant, Mark; Lupton, Gregory; Oprea, John. A mapping theorem for topological complexity. Algebr. Geom. Topol. 15 (2015), no. 3, 1643--1666. doi:10.2140/agt.2015.15.1643. https://projecteuclid.org/euclid.agt/1510840970


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