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 nilpotent 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.
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Received: 12 December 2001 / Published online: 5 September 2002
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Bastardas, G., Descheemaeker, A. On the homotopy type of p-completions of infra-nilmanifolds. Math. Z. 241, 685–696 (2002). https://doi.org/10.1007/s00209-002-0440-8
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DOI: https://doi.org/10.1007/s00209-002-0440-8