## 抄録

Let Y be a connected group and let f : X → Y be a covering map with the total space X being connected. We consider the following question: Is it possible to define a topological group structure on X in such a way that f becomes a homomorphism of topological groups. This holds in some particular cases: if Y is a pathwise connected and locally pathwise connected group or if f is a finite-sheeted covering map over a compact connected group Y . However, using shape-theoretic techniques and Fox's notion of an overlay map, we answer the question in the negative. We consider infinite-sheeted covering maps over solenoids, i.e. compact connected 1-dimensional abelian groups. First we show that an infinite-sheeted covering map f : X → Σ with a total space being connected over a solenoid Σ does not admit a topological group structure on X such that f becomes a homomorphism. Then, for an arbitrary solenoid, we construct a connected space X and an infinite-sheeted covering map f : X →, which provides a negative answer to the question.

本文言語 | English |
---|---|

ページ（範囲） | 69-82 |

ページ数 | 14 |

ジャーナル | Fundamenta Mathematicae |

巻 | 221 |

号 | 1 |

DOI | |

出版ステータス | Published - 2013 |

## ASJC Scopus subject areas

- 代数と数論