Research-A unified approach to Quillen's plus construction, Bousfield localization and zero-in-the-spectrum examples

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A unified approach to Quillen's plus construction, Bousfield localization and zero-in-the-spectrum examples

Speaker: Shengkui Ye （Xi'an Jiaotong-Liverpool University）
Time: Apr 17, 2018, 16:30-17:30
Location: Conference Room 415, Wisdom Valley 3#

We introduce a construction of adding cells to a CW complex preserving homology groups. As applications, we recover the following 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.