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

Katsuya Eda, Vlasta Matijević

    Research output: Contribution to journalArticle

    11 Citations (Scopus)

    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 languageEnglish
    Pages (from-to)1033-1045
    Number of pages13
    JournalTopology and its Applications
    Volume153
    Issue number7
    DOIs
    Publication statusPublished - 2006 Jan 1

    Keywords

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

    ASJC Scopus subject areas

    • Geometry and Topology

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