On 2-dimensional Nonaspherical Cell-like Peano Continua: A Simplified Approach

Katsuya Eda, Umed H. Karimov, Dušan Repovš

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    Abstract

    We construct a functor AC(-, -) from the category of path connected spaces X with a base point x to the category of simply connected spaces. The following are the main results of the paper: (i) If X is a Peano continuum then AC(X, x) is a cell-like Peano continuum; (ii) If X is n-dimensional then AC(X, x) is (n + 1)-dimensional; and (iii) For a path connected space X, π1(X, x) is trivial if and only if π2(AC(X, x)) is trivial. As a corollary, AC(S1, x) is a 2-dimensional nonaspherical cell-like Peano continuum.

    Original languageEnglish
    Pages (from-to)519-528
    Number of pages10
    JournalMediterranean Journal of Mathematics
    Volume10
    Issue number1
    DOIs
    Publication statusPublished - 2013 Feb

    Keywords

    • Alternating cone
    • asphericity
    • cell-like space
    • Noncontractible compactum
    • Peano continuum
    • Snake cone
    • Topologist sine curve
    • trivial shape
    • weak homotopy equivalence

    ASJC Scopus subject areas

    • Mathematics(all)

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