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arXiv · 1312.7166

A Mapping Theorem for Topological Complexity

Mark Grant·Gregory Lupton·John Oprea
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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.

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Mark Grant, Gregory Lupton, John Oprea. 2013-12-27. A Mapping Theorem for Topological Complexity. https://doi.org/10.2140/agt.2015.15.1643

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