On the homotopy type of p-completions of infra-nilmanifolds

Gemma Bastardas, An Descheemaeker

    Research output: Contribution to journalArticleResearchpeer-review

    3 Citations (Scopus)

    Abstract

    Infra-nilmanifolds are compact K(G, 1)-manifolds with G a torsion-free, finitely generated, virtually nilpotent group. Motivated by previous results of various authors on p-completions of K (G, 1)-spaces with G a finite or a nilpotent group, we study the homotopy type of p-completions of infra-nilmanifolds, for any prime p. We prove that the p-completion of an infra-nilmanifold is a virtually nitpotent space which is either aspherical or has infinitely many nonzero homotopy groups. The same is true for p-localization. Moreover, we show by means of examples that rationalizations of infra-nilmanifolds may be elliptic or hyperbolic.
    Original languageEnglish
    Pages (from-to)685-696
    JournalMathematische Zeitschrift
    Volume241
    Issue number4
    DOIs
    Publication statusPublished - 1 Dec 2002

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