### Abstract

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 | |

Publication status | Published - 19 Jun 2015 |

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### Keywords

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

### Cite this

*Algebraic & Geometric Topology*,

*15*(3), 1643-1666. https://doi.org/10.2140/agt.2015.15.1643

**A mapping theorem for topological complexity.** / Grant, Mark; Lupton, Gregory; Oprea, John.

Research output: Contribution to journal › Article

*Algebraic & Geometric Topology*, vol. 15, no. 3, pp. 1643-1666. https://doi.org/10.2140/agt.2015.15.1643

}

TY - JOUR

T1 - A mapping theorem for topological complexity

AU - Grant, Mark

AU - Lupton, Gregory

AU - Oprea, John

PY - 2015/6/19

Y1 - 2015/6/19

N2 - 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.

AB - 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.

KW - Lusternik–Schnirelmann category

KW - sectional category

KW - topological complexity

KW - topological robotics

KW - sectioned fibration

KW - connective cover

KW - Avramov–Félix conjecture

U2 - 10.2140/agt.2015.15.1643

DO - 10.2140/agt.2015.15.1643

M3 - Article

VL - 15

SP - 1643

EP - 1666

JO - Algebraic & Geometric Topology

JF - Algebraic & Geometric Topology

SN - 1472-2747

IS - 3

ER -