The fundamental groups of one-dimensional spaces and spatial homomorphisms

Katsuya Eda

    Research output: Contribution to journalArticle

    18 Citations (Scopus)

    Abstract

    Let X be a one-dimensional metric space and ℍ be the Hawaiian earring.(1) Each homomorphism from π1(ℍ) to π1(X) is induced from a continuous map up to the base-point-change isomorphism on π1(X).(2) Let X be a one-dimensional Peano continuum. Then X has the same homotopy type as that of ℍ if and only if π1(X) is isomorphic to π1(ℍ), if and only if X has a unique point at which X is not semi-locally simply connected. (3) Let X and Y be one-dimensional Peano continua which are not semi-locally simply connected at any point. Then, X and Y are homeomorphic if and only if π1(X) and π1(Y) are isomorphic. Moreover, each isomorphism from π1(X) to π1(Y) is induced by a homeomorphism from X to Y up to the base-point-change-isomorphism.

    Original languageEnglish
    Pages (from-to)479-505
    Number of pages27
    JournalTopology and its Applications
    Volume123
    Issue number3
    DOIs
    Publication statusPublished - 2002 Sep 30

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    Keywords

    • Fundamental group
    • Hawaiian earring
    • One-dimensional
    • Spatial homomorphism

    ASJC Scopus subject areas

    • Geometry and Topology

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