A Mapping Theorem for Topological Complexity
Algebraic Topology
2016-01-20 v1
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.
Cite
@article{arxiv.1312.7166,
title = {A Mapping Theorem for Topological Complexity},
author = {Mark Grant and Gregory Lupton and John Oprea},
journal= {arXiv preprint arXiv:1312.7166},
year = {2016}
}
Comments
22 pages