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A unified approach to the plus-construction, Bousfield localization, Moore spaces and zero-in-the-spectrum examples

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An Erratum to this article was published on 01 August 2013

Abstract

We introduce a construction adding low-dimensional cells to a space that satisfies certain low-dimensional conditions; it preserves high-dimensional homology with appropriate coefficients. This includes as special cases Quillen’s plus construction, Bousfield’s integral homology localization, the existence of Moore spaces M(G, 1) and Bousfield and Kan’s partial k-completion of spaces. We also use it to generalize counterexamples to the zero-in-the-spectrum conjecture found by Farber and Weinberger, and by Higson, Roe and Schick.

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  1. Department of Mathematics, National University of Singapore, Kent Ridge, 119076, Singapore

    Shengkui Ye

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  1. Shengkui Ye
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Correspondence to Shengkui Ye.

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Ye, S. A unified approach to the plus-construction, Bousfield localization, Moore spaces and zero-in-the-spectrum examples. Isr. J. Math. 192, 699–717 (2012). https://doi.org/10.1007/s11856-012-0051-y

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  • DOI: https://doi.org/10.1007/s11856-012-0051-y

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