Postnikov pieces and Bℤ/p-homotopy theory

Natália Castellana, Juan A. Crespo, Jêrôme Scherer

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Abstract

We present a constructive method to compute the cellularization with respect to Bmℤ/p for any integer m ≥ 1 of a large class of H-spaces, namely all those which have a finite number of non-trivial Bmℤ/p-homotopy groups (the pointed mapping space map*(Bmℤ/p,X) is a Postnikov piece). We prove in particular that the Bmℤ/p- cellularization of an H-space having a finite number of Bmℤ/p- homotopy groups is a p-torsion Postnikov piece. Along the way, we characterize the Bℤ/pr-cellular classifying spaces of nilpotent groups. © 2006 American Mathematical Society.
Original languageEnglish
Pages (from-to)1099-1113
JournalTransactions of the American Mathematical Society
Volume359
Issue number3
DOIs
Publication statusPublished - 1 Mar 2007

Keywords

  • Cellularization
  • H-spaces
  • Nilpotent groups.
  • Postnikov pieces

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    Castellana, N., Crespo, J. A., & Scherer, J. (2007). Postnikov pieces and Bℤ/p-homotopy theory. Transactions of the American Mathematical Society, 359(3), 1099-1113. https://doi.org/10.1090/S0002-9947-06-03957-2