|
|||||
|
|
|
|
|
|
|
|
|
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 |
|
|
