### 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 |

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### Keywords

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

### ASJC Scopus subject areas

- Geometry and Topology

### Cite this

*Topology and its Applications*,

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

**Finite sheeted covering maps over 2-dimensional connected, compact Abelian groups.** / Eda, Katsuya; Matijević, Vlasta.

Research output: Contribution to journal › Article

*Topology and its Applications*, vol. 153, no. 7, pp. 1033-1045. https://doi.org/10.1016/j.topol.2005.02.005

}

TY - JOUR

T1 - Finite sheeted covering maps over 2-dimensional connected, compact Abelian groups

AU - Eda, Katsuya

AU - Matijević, Vlasta

PY - 2006/1/1

Y1 - 2006/1/1

N2 - 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.

AB - 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.

KW - 2-dimensional

KW - Compact Abelian group

KW - Compact group

KW - Finite-sheeted covering

UR - http://www.scopus.com/inward/record.url?scp=31844433993&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=31844433993&partnerID=8YFLogxK

U2 - 10.1016/j.topol.2005.02.005

DO - 10.1016/j.topol.2005.02.005

M3 - Article

AN - SCOPUS:31844433993

VL - 153

SP - 1033

EP - 1045

JO - Topology and its Applications

JF - Topology and its Applications

SN - 0166-8641

IS - 7

ER -