Trees, fundamental groups and homology groups

Katsuya Eda, Masasi Higasikawa

    研究成果: Article査読

    1 被引用数 (Scopus)

    抄録

    For a tree T of its height equal to or less than ω1, we construct a space XT by attaching a circle to each node and connecting each node to its successors by intervals. H is the Hawaiian earring and H1 T(X) denotes a canonical factor of the first integral singular homology group. The following equivalences hold for an ω1-tree T: (1) π1(Xω1) is embeddable into π1(XT), if and only if H1 T(X)ω1≃Π ω1 σZ is embeddable into H1 T(XT), if and only if T is not an Aronzajn tree. (2) π1(XT) is embeddable into ××ωZ≃π1(H) if and only if H1 T(XT) is embeddable into Zω≃H1 T(H) if and only if T is a special Aronzajn tree. (3) π1(XT) has a retract isomorphic to an uncountable free group, if and only if H1 T(XT) has a summand isomorphic to an uncountable free abelian group, if and only if T has an uncountable anti-chain.

    本文言語English
    ページ(範囲)185-201
    ページ数17
    ジャーナルAnnals of Pure and Applied Logic
    111
    3
    DOI
    出版ステータスPublished - 2001 8 30

    ASJC Scopus subject areas

    • Logic

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