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2019 A finite $\mathbb{Q}$–bad space
Sergei O Ivanov, Roman Mikhailov
Geom. Topol. 23(3): 1237-1249 (2019). DOI: 10.2140/gt.2019.23.1237

Abstract

We prove that, for a free noncyclic group F , the second homology group H 2 ( F ̂ , ) is an uncountable –vector space, where F ̂ denotes the –completion of F . This solves a problem of A K Bousfield for the case of rational coefficients. As a direct consequence of this result, it follows that a wedge of two or more circles is –bad in the sense of Bousfield–Kan. The same methods as used in the proof of the above result serve to show that H 2 ( F ̂ , ) is not a divisible group, where F ̂ is the integral pronilpotent completion of F .

Citation

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Sergei O Ivanov. Roman Mikhailov. "A finite $\mathbb{Q}$–bad space." Geom. Topol. 23 (3) 1237 - 1249, 2019. https://doi.org/10.2140/gt.2019.23.1237

Information

Received: 27 July 2017; Revised: 29 July 2018; Accepted: 29 September 2018; Published: 2019
First available in Project Euclid: 5 June 2019

zbMATH: 07079058
MathSciNet: MR3956892
Digital Object Identifier: 10.2140/gt.2019.23.1237

Subjects:
Primary: 14F35, 16W60, 55P60

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.23 • No. 3 • 2019
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