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Existence of finitely dominatedCW-complexes withG 1(X) = π1(X) and non-vanishing finiteness obstruction

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Abstract

We show for a finite abelian groupG and any element in the image of the Swan homomorphism sw:\(\mathbb{Z}/|G|* \to \tilde K_0 (\mathbb{Z}G)\) that it can be realized as the finiteness obstruction of a finitely dominated connectedCW-complexX with fundamental group π1(X) =G such that π1(X) is equal to the subgroupG 1(X) defined by Gottlieb. This is motivated by the observation that anyH-spaceX satisfies π1(X) =G 1(X) and still the problem is open whether any finitely dominatedH-space is up to homotopy finite.

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  1. Fachbereich für Mathematik und Informatik, Westfälische Wilhelms-Universität Münster, Einsteinstr. 62, 48149, Münster, Germany

    Wolfgang Lück & Andreas Müller

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  1. Wolfgang Lück
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  2. Andreas Müller
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Lück, W., Müller, A. Existence of finitely dominatedCW-complexes withG 1(X) = π1(X) and non-vanishing finiteness obstruction. Manuscripta Math 93, 535–538 (1997). https://doi.org/10.1007/BF02677490

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  • DOI: https://doi.org/10.1007/BF02677490

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