A Mapping Theorem for Topological Complexity

Authors

Mark Grant, Newcastle University
Gregory Lupton, Cleveland State UniversityFollow
John Oprea, Cleveland State UniversityFollow

Document Type

Article

Publication Date

2015

Publication Title

Algebraic and Geometric Topology

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.

Comments

This work was partially supported by grants from the Simons Foundation: (#209575 to Gregory Lupton and #244393 to John Oprea).

Repository Citation

Grant, Mark; Lupton, Gregory; and Oprea, John, "A Mapping Theorem for Topological Complexity" (2015). Mathematics and Statistics Faculty Publications. 122.
https://engagedscholarship.csuohio.edu/scimath_facpub/122

DOI

10.2140/agt.2015.15.1643

Version

Publisher's PDF

Volume

15

Issue

3