Algebraic and Geometric Topology
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.
Grant, Mark; Lupton, Gregory; and Oprea, John, "A Mapping Theorem for Topological Complexity" (2015). Mathematics Faculty Publications. 122.