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.
Citation
Mark Grant. Gregory Lupton. John Oprea. "A mapping theorem for topological complexity." Algebr. Geom. Topol. 15 (3) 1643 - 1666, 2015. https://doi.org/10.2140/agt.2015.15.1643
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