Geodesic
A mapping theorem for topological complexity
Grant, Mark1 ; Lupton, Gregory2 ; Oprea, John2
1Institute of Pure and Applied Mathematics, University of Aberdeen, Fraser Noble Building, Aberdeen, AB24 3UE, UK
2Department of Mathematics, Cleveland State University, 2121 Euclid Avenue, Cleveland, OH 44115, USA
Algebraic and Geometric Topology, Tome 15 (2015) no. 3, pp. 1643-1666
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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.

DOI : 10.2140/agt.2015.15.1643
Classification : 55M30, 55P62, 55S40, 55Q15
Keywords: Lusternik–Schnirelmann category, sectional category, topological complexity, topological robotics, sectioned fibration, connective cover, Avramov–Félix conjecture

Grant, Mark  1   ; Lupton, Gregory  2   ; Oprea, John  2

1 Institute of Pure and Applied Mathematics, University of Aberdeen, Fraser Noble Building, Aberdeen, AB24 3UE, UK
2 Department of Mathematics, Cleveland State University, 2121 Euclid Avenue, Cleveland, OH 44115, USA 
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Grant, Mark; Lupton, Gregory; Oprea, John. A mapping theorem for topological complexity. Algebraic and Geometric Topology, Tome 15 (2015) no. 3, pp. 1643-1666. doi: 10.2140/agt.2015.15.1643

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