Algebraic & Geometric Topology

A mapping theorem for topological complexity

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
Revised: 21 October 2014
Accepted: 23 October 2014
First available in Project Euclid: 16 November 2017

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

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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