### Abstract

Let G be a 2-dimensional connected, compact Abelian group and s be a positive integer. We prove that a classification of s-sheeted covering maps over G is reduced to a classification of s-index torsionfree supergroups of the Pontrjagin dual Ĝ. Using group theoretic results from earlier paper we demonstrate its consequences. We also prove that for a connected compact group Y: (1) Every finite-sheeted co vering map from a connected space over Y is equivalent to a covering homomorphism from a compact, connected group. (2) If two finite-sheeted covering homomorphisms over Y are equivalent, then they are equivalent as topological homomorphisms.

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

Pages (from-to) | 1033-1045 |

Number of pages | 13 |

Journal | Topology and its Applications |

Volume | 153 |

Issue number | 7 |

DOIs | |

Publication status | Published - 2006 Jan 1 |

### Keywords

- 2-dimensional
- Compact Abelian group
- Compact group
- Finite-sheeted covering

### ASJC Scopus subject areas

- Geometry and Topology

## Fingerprint Dive into the research topics of 'Finite sheeted covering maps over 2-dimensional connected, compact Abelian groups'. Together they form a unique fingerprint.

## Cite this

Eda, K., & Matijević, V. (2006). Finite sheeted covering maps over 2-dimensional connected, compact Abelian groups.

*Topology and its Applications*,*153*(7), 1033-1045. https://doi.org/10.1016/j.topol.2005.02.005