Existence and uniqueness of group structures on covering spaces over groups

Katsuya Eda, Vlasta Matijević

    Research output: Contribution to journal › Article

    Abstract

    Let f : X → Y be a covering map from a connected space X onto a topological group Y and let x0 ∈ X be a point such that f(x0) is the identity of Y: We examine if there exists a group operation on X which makes X a topological group with identity x0 and f a homomorphism of groups. We prove that the answer is positive in two cases: if f is an overlay map over a locally compact group Y, and if Y is locally compactly connected. In this way we generalize previous results for overlay maps over compact groups and covering maps over locally path-connected groups. Furthermore, we prove that in both cases the group structure on X is unique.

    Original languageEnglish
    Pages (from-to)241-267
    Number of pages27
    JournalFundamenta Mathematicae
    Volume238
    Issue number3
    DOIs
    Publication statusPublished - 2017

    Fingerprint

    Covering Space
    Existence and Uniqueness
    Covering Map
    Topological group
    Overlay
    Locally Connected
    Locally Compact Group
    Compact Group
    Homomorphism
    Path
    Generalise

    Keywords

    • Abelian group
    • Compact group
    • Compactly connected space
    • Covering homomorphism
    • Covering map
    • Locally compact group
    • Locally compactly connected space
    • Overlay map
    • Topological group

    ASJC Scopus subject areas

    • Algebra and Number Theory

    Cite this

    Existence and uniqueness of group structures on covering spaces over groups. / Eda, Katsuya; Matijević, Vlasta.

    In: Fundamenta Mathematicae, Vol. 238, No. 3, 2017, p. 241-267.

    Research output: Contribution to journal › Article

    Eda, K & Matijević, V 2017, 'Existence and uniqueness of group structures on covering spaces over groups', Fundamenta Mathematicae, vol. 238, no. 3, pp. 241-267. https://doi.org/10.4064/fm990-10-2016
    Eda K, Matijević V. Existence and uniqueness of group structures on covering spaces over groups. Fundamenta Mathematicae. 2017;238(3):241-267. https://doi.org/10.4064/fm990-10-2016
    Eda, Katsuya ; Matijević, Vlasta. / Existence and uniqueness of group structures on covering spaces over groups. In: Fundamenta Mathematicae. 2017 ; Vol. 238, No. 3. pp. 241-267.
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