A mapping theorem for topological complexity

Mark Grant; Gregory Lupton; John Oprea

doi:10.2140/agt.2015.15.1643

A mapping theorem for topological complexity

Mark Grant, Gregory Lupton, John Oprea

Mathematical Science

Cleveland State University

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

9 Downloads (Pure)

Abstract

We give new lower bounds for the (higher) topological complexity of a space, in terms of the LusternikSchnirelmann 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.

Original language	English
Pages (from-to)	1643-1666
Number of pages	24
Journal	Algebraic & Geometric Topology
Volume	15
Issue number	3
Early online date	19 Jun 2015
DOIs	https://doi.org/10.2140/agt.2015.15.1643
Publication status	Published - 19 Jun 2015

Keywords

Lusternik–Schnirelmann category
sectional category
topological complexity
topological robotics
sectioned fibration
connective cover
Avramov–Félix conjecture

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A mapping theorem for topological complexity
First published in Algebraic & Geometric Topology in Vol. 15(3), published by Mathematical Sciences Publishers
Final published version, 390 KB

Cite this

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KW - sectional category

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KW - topological robotics

KW - sectioned fibration

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A mapping theorem for topological complexity

Abstract

Keywords

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