English

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