On Finite domination and Poincaré duality

The object of this paper is to show that non-homotopy finite Poincaré duality spaces are plentiful. Let $π$ be finitely presented group. Assuming that the reduced Grothendieck group $\tilde K_0(\Bbb Z[π])$ has a non-trivial 2-divisible element, we construct a finitely dominated Poincaré space $X$ with fundamental group $π$ such that $X$ is not homotopy finite. The dimension of $X$ can be made arbitrarily large. Our proof relies on a result which says that every finitely dominated space possesses a stable Poincaré duality thickening.

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