A unified approach to the plus-construction, Bousfield localization, Moore spaces and zero-in-the-spectrum examples
K-Theory and Homology
2013-01-30 v2 Algebraic Topology
Geometric Topology
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.
Keywords
Cite
@article{arxiv.1107.3392,
title = {A unified approach to the plus-construction, Bousfield localization, Moore spaces and zero-in-the-spectrum examples},
author = {Shengkui Ye},
journal= {arXiv preprint arXiv:1107.3392},
year = {2013}
}
Comments
final version with an erratum on G-dense rings