### Abstract

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

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 |

### Keywords

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

## Fingerprint Dive into the research topics of 'Hopf invariants, topological complexity, and LS-category of the cofiber of the diagonal map for two-cell complexes'. Together they form a unique fingerprint.

## Cite this

González, J., Grant, M., & Vandembroucq, L. (2018). Hopf invariants, topological complexity, and LS-category of the cofiber of the diagonal map for two-cell complexes. In M. Grant, G. Lupton, & L. Vandembroucq (Eds.),

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