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

• Autores: J. A. Hillman, Dessislava H. Kochloukova
• Localización: Mathematische zeitschrift, ISSN 0025-5874, Vol. 256, Nº. 1, 2007, págs. 45-56
• Idioma: inglés
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• Resumen

  • We show that an infinite cyclic covering space M' of a PD n -complex M is a PD n-1-complex if and only if ?(M) = 0, M' is homotopy equivalent to a complex with finite [(n-1)/2]-skeleton and p1(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 ? with covering group a PD r -group under a slightly stricter finiteness condition