A finite Q-bad space

Sergei O. Ivanov, Roman Mikhailov

    Research output

    Abstract

    We prove that, for a free noncyclic group F, the second homology group H2(FQ;Q/ is an uncountable Q-vector space, where FQ denotes the Q-completion of F. This solves a problem of AK 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 Q-bad in the sense of Bousfield-Kan. The same methods as used in the proof of the above result serve to show that H2 (FZ, Z) is not a divisible group, where FZ is the integral pronilpotent completion of F.

    Original languageEnglish
    Pages (from-to)1237-1249
    Number of pages13
    JournalGeometry and Topology
    Volume23
    Issue number3
    DOIs
    Publication statusPublished - 1 Jan 2019

    Fingerprint

    Completion
    Homology Groups
    Uncountable
    Divisible
    Wedge
    Free Group
    Vector space
    Circle
    Denote
    Coefficient

    Scopus subject areas

    • Geometry and Topology

    Cite this

    Ivanov, S. O., & Mikhailov, R. (2019). A finite Q-bad space. Geometry and Topology, 23(3), 1237-1249. https://doi.org/10.2140/gt.2019.23.1237
    Ivanov, Sergei O. ; Mikhailov, Roman. / A finite Q-bad space. In: Geometry and Topology. 2019 ; Vol. 23, No. 3. pp. 1237-1249.
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    Ivanov, SO & Mikhailov, R 2019, 'A finite Q-bad space', Geometry and Topology, vol. 23, no. 3, pp. 1237-1249. https://doi.org/10.2140/gt.2019.23.1237

    A finite Q-bad space. / Ivanov, Sergei O.; Mikhailov, Roman.

    In: Geometry and Topology, Vol. 23, No. 3, 01.01.2019, p. 1237-1249.

    Research output

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    Ivanov SO, Mikhailov R. A finite Q-bad space. Geometry and Topology. 2019 Jan 1;23(3):1237-1249. https://doi.org/10.2140/gt.2019.23.1237