Finiteness conditions and PDr-group covers of PDn-complexes

J.A. Hillman and D.H. Kochloukova


We show that an infinite cyclic covering space M' of a PDn-complex M is a PDn-1-complex if and only if χ(M)=0 and M' is homotopy equivalent to a complex with finite [(n-1)/2]-skeleton and ν=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 Mν with covering group a PDr-group π1(M)/ν under a slightly stricter finiteness condition.

Keywords: coinduced module, finiteness condition, finite domination, infinite cyclic cover, Novikov ring, Poincaré duality.

AMS Subject Classification: Primary 57P10; secondary 55R99.

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Tuesday, July 12, 2005