### Abstract

Original language | English |
---|---|

Title of host publication | Topological complexity and related topics |

Editors | Mark Grant, Gregory Lupton, Lucile Vandembroucq |

Publisher | American Mathematical Society |

Pages | 133-150 |

Number of pages | 18 |

Volume | 702 |

ISBN (Electronic) | 9781470444051 |

ISBN (Print) | 9781470434366 |

DOIs | |

Publication status | Published - 2018 |

### Publication series

Name | Contemporary Mathematics |
---|---|

Publisher | American Mathematical Society |

ISSN (Print) | 1098-3627 |

ISSN (Electronic) | 0271-4132 |

### Fingerprint

### Keywords

- math.AT
- 55M30, 55Q25, 55S35, 55S36, 68T40, 70B15

### Cite this

*Topological complexity and related topics*(Vol. 702, pp. 133-150). (Contemporary Mathematics). American Mathematical Society. https://doi.org/10.1090/conm/702/14109

**Hopf invariants, topological complexity, and LS-category of the cofiber of the diagonal map for two-cell complexes.** / González, Jesús; Grant, Mark; Vandembroucq, Lucile.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Topological complexity and related topics.*vol. 702, Contemporary Mathematics, American Mathematical Society, pp. 133-150. https://doi.org/10.1090/conm/702/14109

}

TY - GEN

T1 - Hopf invariants, topological complexity, and LS-category of the cofiber of the diagonal map for two-cell complexes

AU - González, Jesús

AU - Grant, Mark

AU - Vandembroucq, Lucile

PY - 2018

Y1 - 2018

N2 - Let $X$ be a two-cell complex with attaching map $\alpha\colon S^q\to S^p$, and let $C_X$ be the cofiber of the diagonal inclusion $X\to X\times X$. It is shown that the topological complexity (${\rm TC}$) of $X$ agrees with the Lusternik-Schnirelmann category (${\rm cat}$) of $C_X$ in the (almost stable) range $q\leq2p-1$. In addition, the equality ${\rm TC}(X)={\rm cat}(C_X)$ is proved in the (strict) metastable range $2p-1

AB - Let $X$ be a two-cell complex with attaching map $\alpha\colon S^q\to S^p$, and let $C_X$ be the cofiber of the diagonal inclusion $X\to X\times X$. It is shown that the topological complexity (${\rm TC}$) of $X$ agrees with the Lusternik-Schnirelmann category (${\rm cat}$) of $C_X$ in the (almost stable) range $q\leq2p-1$. In addition, the equality ${\rm TC}(X)={\rm cat}(C_X)$ is proved in the (strict) metastable range $2p-1

KW - math.AT

KW - 55M30, 55Q25, 55S35, 55S36, 68T40, 70B15

U2 - 10.1090/conm/702/14109

DO - 10.1090/conm/702/14109

M3 - Conference contribution

SN - 9781470434366

VL - 702

T3 - Contemporary Mathematics

SP - 133

EP - 150

BT - Topological complexity and related topics

A2 - Grant, Mark

A2 - Lupton, Gregory

A2 - Vandembroucq, Lucile

PB - American Mathematical Society

ER -