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Finiteness conditions and PD r -group covers of PD n -complexes

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We show that an infinite cyclic covering space M′ of a PD n -complex M is a PDn-1-complex if and only if χ(M) = 0, M′ is homotopy equivalent to a complex with finite [(n−1)/2]-skeleton and π1(M′) is finitely presentable. This is best possible in terms of minimal finiteness assumptions on the covering space. We give also a corresponding result for covering spaces M ν with covering group a PD r -group under a slightly stricter finiteness condition.

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Authors and Affiliations

  1. School of Mathematics and Statistics, University of Sydney, Sydney, NSW, 2006, Australia

    J. A. Hillman

  2. UNICAMP-IMECC, Cx.P.6065, Campinas, SP, 13083-970, Brazil

    D. H. Kochloukova

Authors
  1. J. A. Hillman
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  2. D. H. Kochloukova
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Correspondence to J. A. Hillman.

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Hillman, J.A., Kochloukova, D.H. Finiteness conditions and PD r -group covers of PD n -complexes. Math. Z. 256, 45–56 (2007). https://doi.org/10.1007/s00209-006-0058-3

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  • DOI: https://doi.org/10.1007/s00209-006-0058-3

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