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

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

2011-07-18

arxiv.org/abs/1107.3392v1

Mathematics

K-Theory and Homology

21 pages, to appear in Israel Journal of Mathematics (2012)

Scientific paper

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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