## Abstract

Given a fixed "model space" M, we call a map f: X-+ Y an M-equivalence if it induces a weak equivalence f.: xM-+ yM on mapping spaces. We discuss the following question: under what conditions do homotopy colimits preserve M-equivalences? For certain M's of interest,

this is shown to depend precisely on the connectivities of the spaces.

this is shown to depend precisely on the connectivities of the spaces.

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

Title of host publication | The Čech Centennial |

Subtitle of host publication | A Conference on Homotopy Theory |

Editors | Jonathan Rosenberg, Stephan Stolz |

Publisher | American Mathematical Society |

Pages | 27–33 |

Number of pages | 7 |

ISBN (Electronic) | 978-0-8218-7772-2 |

ISBN (Print) | 978-0-8218-0296-0, 0-8218-0296-8 |

DOIs | |

State | Published - 1995 |

### Publication series

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

Publisher | American Mathematical Society |

Number | 181 |

## Keywords

- Combinatorics
- Cyclic group
- Fundamental group
- Group (mathematics)
- Manifold
- Mathematics
- Order (group theory)
- Scalar curvature
- Simply connected space
- Trivial group