On snake cones, alternating cones and related constructions

Katsuya Eda, Umed H. Karimov, Dušan Repovš, Andreas Zastrow

    Research output: Contribution to journalArticle

    Abstract

    We show that the Snake on a square SC(S1) is homotopy equivalent to the space AC(S1) which was investigated in the previous work by Eda, Karimov and Repovš. We also introduce related constructions CSC(-) and CAC(-) and investigate homotopical differences between these four constructions. Finally, we explicitly describe the second homology group of the Hawaiian tori wedge.

    Original languageEnglish
    Pages (from-to)115-135
    Number of pages21
    JournalGlasnik Matematicki
    Volume48
    Issue number1
    DOIs
    Publication statusPublished - 2013

    Keywords

    • Asphericity
    • Collapsed alternating cone
    • Collapsed snake cone
    • Hawaiian earring
    • Hawaiian tori
    • Noncontractible compactum
    • Peano continuum
    • Snake on a square
    • Topologist sine curve
    • Trivial shape
    • Weak homotopy equivalence

    ASJC Scopus subject areas

    • Mathematics(all)

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  • Cite this

    Eda, K., Karimov, U. H., Repovš, D., & Zastrow, A. (2013). On snake cones, alternating cones and related constructions. Glasnik Matematicki, 48(1), 115-135. https://doi.org/10.3336/gm.48.1.11