Algebraic topology of Peano continua

Katsuya Eda

    Research output: Contribution to journalArticle

    7 Citations (Scopus)

    Abstract

    Let X be a Peano continuum. Then the following hold: (1) The singular cohomology group H1(X) is isomorphic to the Čech cohomology group Ȟ1(X). (2) For each homomorphism h: π1(X) → *i∈I Gi there exists a finite subset F of I such that Im(h) ⊆ *i∈F Gi. (3) For each injective homomorphism h: π1(X) → G0 * G1 there exists a finitely generated subgroup F0 of G0 or a finitely generated subgroup F1 of G1 such that Im(h) ⊆ F0 * G1 or Im(h) ⊆ G0 * F1.

    Original languageEnglish
    Pages (from-to)213-226
    Number of pages14
    JournalTopology and its Applications
    Volume153
    Issue number2-3 SPEC. ISS.
    DOIs
    Publication statusPublished - 2005 Sep 1

    Keywords

    • Fundamental group
    • Homology group
    • Peano continua

    ASJC Scopus subject areas

    • Geometry and Topology

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