Maps from the minimal grope to an arbitrary grope

Matija Cencelj, Katsuya Eda, Aleš Vavpetič

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    Abstract

    We consider open infinite gropes and prove that every continuous map from the minimal grope to another grope is nulhomotopic unless the other grope has a «branch» which is a copy of the minimal grope. Since every grope is the classifying space of its fundamental group, the problem is translated to group theory and a suitable block cancellation of words is used to obtain the result.

    Original languageEnglish
    Pages (from-to)503-519
    Number of pages17
    JournalInternational Journal of Algebra and Computation
    Volume23
    Issue number3
    DOIs
    Publication statusPublished - 2013 May

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    Keywords

    • Grope
    • perfect group

    ASJC Scopus subject areas

    • Mathematics(all)

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