Existence and uniqueness of group structures on covering spaces over groups

Katsuya Eda, Vlasta Matijević

    研究成果: Article査読

    2 被引用数 (Scopus)

    抄録

    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.

    本文言語English
    ページ(範囲)241-267
    ページ数27
    ジャーナルFundamenta Mathematicae
    238
    3
    DOI
    出版ステータスPublished - 2017

    ASJC Scopus subject areas

    • Algebra and Number Theory

    フィンガープリント 「Existence and uniqueness of group structures on covering spaces over groups」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

    引用スタイル